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1krw6css0 | physics | motion-in-a-straight-line | variable-acceleration-motion | The relation between time t and distance x for a moving body is given as t = mx<sup>2</sup> + nx, where m and n are constants. The retardation of the motion is : (When v stands for velocity) | [{"identifier": "A", "content": "2 mv<sup>3</sup>"}, {"identifier": "B", "content": "2 mnv<sup>3</sup>"}, {"identifier": "C", "content": "2nv<sup>3</sup>"}, {"identifier": "D", "content": "2n<sup>2</sup>v<sup>3</sup>"}] | ["A"] | null | <p>The relationship between time $ t $ and distance $ x $ for a moving body is given by $ t = mx^2 + nx $, where $ m $ and $ n $ are constants. To determine the retardation (negative acceleration) of the motion, let's follow the steps to derive it:</p>
<p>Given:</p>
<p>$ t = mx^2 + nx $</p>
<p>First, differentiate $... | mcq | jee-main-2021-online-25th-july-evening-shift | 12,172 |
1l6f5g0ka | physics | motion-in-a-straight-line | variable-acceleration-motion | <p>A particle is moving in a straight line such that its velocity is increasing at 5 ms<sup>$$-$$1</sup> per meter. The acceleration of the particle is _____________ ms<sup>$$-$$2</sup> at a point where its velocity is 20 ms<sup>$$-$$1</sup>.</p> | [] | null | 100 | <p>$${{dv} \over {dx}} = 5$$ ms<sup>$$-$$1</sup>/m</p>
<p>Acceleration of particle</p>
<p>when $$v = 20$$ m/s</p>
<p>$$a = v{{dv} \over {dx}} = 20(5)$$ m/s<sup>2</sup> = 100 m/s<sup>2</sup></p> | integer | jee-main-2022-online-25th-july-evening-shift | 12,173 |
lsanbcwk | physics | motion-in-a-straight-line | variable-acceleration-motion | A particle initially at rest starts moving from reference point $x=0$ along $x$-axis, with velocity $v$ that varies as $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The acceleration of the particle is __________ $\mathrm{ms}^{-2}$. | [] | null | 8 | <p>To find the acceleration of the particle, we first need to differentiate the velocity function with respect to time. The velocity function given is</p>
<p>$$ v = 4\sqrt{x} $$</p>
<p>However, this function gives the velocity as a function of position $x$, not as a function of time $t$. Since acceleration is the rate ... | integer | jee-main-2024-online-1st-february-evening-shift | 12,174 |
lsblif93 | physics | motion-in-a-straight-line | variable-acceleration-motion | A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$, where $x$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$. <br/><br/>The... | [] | null | 52 | <ul>
<li><strong>Position (x):</strong> The particle's location on the x-axis at a given time.</li><br>
<li><strong>Velocity (v):</strong> The rate of change of position with respect to time</li>
</ul>
<p>( $v = \frac{dx}{dt}$ ).</p>
<ul>
<li><strong>Acceleration (a):</strong> The rate of change of velocity with respe... | integer | jee-main-2024-online-1st-february-morning-shift | 12,175 |
3xRnUDU1F67DjjNy | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is | [{"identifier": "A", "content": "inversely proportional to both radius $$R$$ and velocity $$v$$ "}, {"identifier": "B", "content": "directly proportional to both radius $$R$$ and velocity $$v$$ "}, {"identifier": "C", "content": "directly proportional to $$R$$ but inversely proportional to $$v$$ "}, {"identifier": "D",... | ["B"] | null | From Stoke's law,
<br><br>viscous force acting on the ball falling into a viscous fluid
<br><br>$$F = 6\pi \eta Rv$$
<br><br>$$\therefore$$ $$F \propto R$$ and $$F \propto v$$
<br><br>hence $$F$$ is directly proportional to radius & velocity. | mcq | aieee-2004 | 12,179 |
sVk2AaQkeLyh6qNm | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | If the terminal speed of a sphere of gold (density $$ = 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (density $$ = 1.5\,\,kg/{m^3}$$, find the terminal speed of a sphere of silver (density $$ = 10.5\,\,kg/{m^3}$$) of the same size in the same liquid | [{"identifier": "A", "content": "$$0.4$$ $$m/s$$ "}, {"identifier": "B", "content": "$$0.133$$ $$m/s$$ "}, {"identifier": "C", "content": "$$0.1$$ $$m/s$$ "}, {"identifier": "D", "content": "$$0.2$$ $$m/s$$ "}] | ["C"] | null | Let Terminal velocity = v<sub>t</sub>
<br><br>Upward viscous force = downward weight of sphere
<br><br>$$ \Rightarrow 6\pi \eta r{v_t} = \left( {{4 \over 3}\pi {r^3}} \right)\left( {\rho - \sigma } \right)g$$
<br><br>$$ \Rightarrow {v_t} = {{2{r^2}\left( {\rho - \sigma } \right)g} \over {9\eta }}$$ ........ (1)
<br><... | mcq | aieee-2006 | 12,180 |
uq8SZDqVxZWn6vtw | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of density $${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $$v,$$ i.e., $${F_{viscous}}... | [{"identifier": "A", "content": "$$\\sqrt {{{Vg\\left( {{\\rho _1} - {\\rho _2}} \\right)} \\over k}} $$ "}, {"identifier": "B", "content": "$${{{Vg{\\rho _1}} \\over k}}$$ "}, {"identifier": "C", "content": "$$\\sqrt {{{Vg{\\rho _1}} \\over k}} $$ "}, {"identifier": "D", "content": "$${{Vg\\left( {{\\rho _1} - {\\rho ... | ["A"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266105/exam_images/zrw8zlkblio7srvhbfes.webp" loading="lazy" alt="AIEEE 2008 Physics - Properties of Matter Question 238 English Explanation">
<br>The forces acting on the ball -
<br><br>(1) mg = $$V{\rho _1}g$$ downward direction
... | mcq | aieee-2008 | 12,181 |
a1gAWb3hDAhAJ0QG | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Water is flowing continuously from a tap having an internal diameter $$8 \times {10^{ - 3}}\,\,m.$$ The water velocity as it leaves the tap is $$0.4\,\,m{s^{ - 1}}$$ . The diameter of the water stream at a distance $$2 \times {10^{ - 1}}\,\,m$$ below the tap is close to : | [{"identifier": "A", "content": "$$7.5 \\times {10^{ - 3}}m$$ "}, {"identifier": "B", "content": "$$9.6 \\times {10^{ - 3}}m$$ "}, {"identifier": "C", "content": "$$3.6 \\times {10^{ - 3}}m$$ "}, {"identifier": "D", "content": "$$5.0 \\times {10^{ - 3}}m$$ "}] | ["C"] | null | From Bernoulli's theorem,
<br>$${P_0} + {1 \over 2}\rho v_1^2\rho gh = {P_0} + {1 \over 2}\rho v_2^2 + 0$$
<br>$${v_2} = \sqrt {v_1^2 + 2gh} $$
<br>$$ = \sqrt {0.16 + 2 \times 10 \times 0.2} $$
<br>$$ = 2.03\,m/s$$
<br>From equation of continuity
<br>$${A_2}{v_2} = {A_1}{v_1}$$
<br>$$\pi {{D_2^2} \over 4} \times {v_2} ... | mcq | aieee-2011 | 12,182 |
LhGCtS2aeU160MtE | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $$R$$ and making a circular contact of radius $$r$$ with the bottom $$R$$ and making a circular contact of radius $$r$$ with the bottom of the vessel. If $$r < < R$$ and the surface tensio... | [{"identifier": "A", "content": "$${R^2}\\sqrt {{{{\\rho _w}g} \\over {3T}}} $$ "}, {"identifier": "B", "content": "$${R^2}\\sqrt {{{{\\rho _w}g} \\over {6T}}} $$ "}, {"identifier": "C", "content": "$${R^2}\\sqrt {{{{\\rho _w}g} \\over {T}}} $$"}, {"identifier": "D", "content": "$${R^2}\\sqrt {{{{2\\rho _w}g} \\over {3... | ["D"] | null | When the bubble gets detached, Buoyant force $$=$$ force due to surface tension
<br><img class="question-image" src="https://imagex.cdn.examgoal.net/4opxg7CIM1cnXllBE/PScFKI5eBj7YljehjKHkERwF9abNK/rSO7r9I8VzLo9cmM42UBcV/image.svg" loading="lazy" alt="JEE Main 2014 (Offline) Physics - Properties of Matter Question 226 E... | mcq | jee-main-2014-offline | 12,183 |
zKYU4HvflG95ynDXapiDJ | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <img src="data:image/png;base64,UklGRtYRAABXRUJQVlA4IMoRAACw7wCdASreAQADP4G+2mM2MLqmIhGqg1AwCWlu/AkYSvynZ17/sz/p/Vxcfr4sN7QT+s/WH//+d+Iog19Kv/vQC9mP+3nn//9/+9qv//1SffIyuFZxtXm1eZ8X2p30yaksEVaZ8FjQSL9pkICzSeRdPIunjp+wAOd+y+22rBm4jK8mcbV5tVvKGifyLp5F08Z7gLlPvpCIrr+N+eHUDGQff99cuDOb5jFy0iF6du8rem2YjIesOmub7ldgLNJ5Fzwd+C0W... | [{"identifier": "A", "content": "$$x = r\\left( {{H \\over {H + h}}} \\right)$$"}, {"identifier": "B", "content": "$$x = r{\\left( {{H \\over {H + h}}} \\right)^{{1 \\over 2}}}$$ "}, {"identifier": "C", "content": "$$x = r{\\left( {{H \\over {H + h}}} \\right)^{{1 \\over 4}}}$$"}, {"identifier": "D", "content": "$$x = ... | ["C"] | null | v<sub>1</sub> = velocity of water when it leak from hole
<br><br>v<sub>2</sub> = velocity of water when it reach the ground.
<br><br>From Bernoulli's principle,
<br><br>$${1 \over 2}\rho {v_1}^2 + \rho gh$$ = $${1 \over 2}\rho {v_2}^2$$
<br><br>$$ \Rightarrow $$ $${v_1}^2$$ + 2gh = $${v_2}^2$$
<br><br>... | mcq | jee-main-2016-online-9th-april-morning-slot | 12,184 |
fe8pGKnjARWzPcjj0mZcg | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Which of the following option correctly describes the variation of the speed <i>v</i> and acceleration <i>‘a’</i> of a point mass falling vertically in a viscous medium that applies a force F = − <i>kv,</i> where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale) | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l80ytcdy/e1321622-f3ca-4335-8dea-e66791c45488/7f6a1960-33cf-11ed-bcbd-5353ee2ab2b1/file-1l80ytcdz.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l80ytcdy/e1321622-f3ca-4335-8dea-e66791c45488/7f6... | ["B"] | null | Equation of motion for the mass,
<br><br>ma = mg $$-$$ kv
<br><br>$$ \Rightarrow $$ $${{dv} \over {dt}} = {{mg - kv} \over m}$$
<br><br>$$ \Rightarrow $$ $$\int\limits_0^v {{{dv} \over {mg - kv}}} = {1 \over m}\int\limits_0^t {dt} $$
<br><br>$$ \Rightarrow $$ $$ - {1... | mcq | jee-main-2016-online-9th-april-morning-slot | 12,185 |
lDWnjJ6foMzKFqoMnliOq | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Two tubes of radii r<sub>1</sub> and r<sub>2</sub>, and lengths l<sub>1</sub> and l<sub>2</sub> , respectively, are connected in series
and a liquid flows through each of them in stream line conditions. P<sub>1</sub> and P<sub>2</sub> are pressure differences across the two tubes.
<br/><br/>If P<sub>2</sub> is 4P<... | [{"identifier": "A", "content": "r<sub>1</sub>"}, {"identifier": "B", "content": "2r<sub>1</sub>"}, {"identifier": "C", "content": "4r<sub>1</sub> "}, {"identifier": "D", "content": "$${{{r_1}} \\over 2}$$ "}] | ["D"] | null | We know,
<br><br>Rate of flow of liquid through narrow tube,
<br><br>$${{dv} \over {dt}}$$ = $${{\pi {{\Pr }^4}} \over {8\eta l}}$$
<br><br>Both tubes are connected in series so rate of flow of liquid is same.
<br><br>$$\therefore\,\,\,$$ $${{\pi {P_1}r_1^4} \over {8\eta {l_1}}}$$ = $${{\pi {P_2}r_2^4} \over {8\et... | mcq | jee-main-2017-online-9th-april-morning-slot | 12,186 |
6b3uqOdsIiRkTBUOom2VA | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | The top of a water tank is open to air and its water level is mainted. It is giving out 0.74 m<sup>3</sup> water per minute through a circular opening of 2 cm radius in its wall. The depth of the center of the opening from the level of water in the tank is close to : | [{"identifier": "A", "content": "6.0 m"}, {"identifier": "B", "content": "4.8 m"}, {"identifier": "C", "content": "9.6 m"}, {"identifier": "D", "content": "2.9 m"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264023/exam_images/acylrfqpyefqghujddnj.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Evening Slot Physics - Properties of Matter Question 209 English Explanation">
<br><... | mcq | jee-main-2019-online-9th-january-evening-slot | 12,187 |
lcunR0RKhClnAONLIE5Ep | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Water flows into a large tank with flat bottom at the rate of 10<sup>–4</sup>m<sup>3</sup>s<sup>–1</sup>. Water is also leaking out of a hole ofarea 1 cm<sup>2</sup> at its bottom. If the height of the water in the tank remains steady, then this height is - | [{"identifier": "A", "content": "2.9 cm"}, {"identifier": "B", "content": "5.1 cm"}, {"identifier": "C", "content": "4 cm"}, {"identifier": "D", "content": "1.7 cm"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264556/exam_images/jobn01pgowiqxeko3cbs.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 10th January Morning Slot Physics - Properties of Matter Question 208 English Explanation">
<br>... | mcq | jee-main-2019-online-10th-january-morning-slot | 12,188 |
rxt0Fog6gwyvaU1QQ4b5p | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Water from a pipe is coming at a rate of
100 litres per minute. If the radius of the pipe
is 5 cm, the Reynolds number for the flow is
of the order of : (density of water = 1000 kg/m<sup>3</sup>,
coefficient of viscosity of water = 1mPas) | [{"identifier": "A", "content": "10<sup>6</sup>"}, {"identifier": "B", "content": "10<sup>4</sup>"}, {"identifier": "C", "content": "10<sup>3</sup>"}, {"identifier": "D", "content": "10<sup>2</sup>"}] | ["B"] | null | Flow rate of water (Q) = 100 lit/min<br><br>
= $${{100 \times {{10}^{ - 3}}} \over {60}} = {5 \over 3} \times {10^{ - 3}}{m^3}$$<br><br>
$$ \therefore $$ Velocity of flow (v)<br><br> = $${Q \over A} = {{5 \times {{10}^{ - 3}}} \over {3 \times \pi \times {{(5 \times {{10}^{ - 2}})}^2}}}$$<br><br>
$$ = {{10} \over {15\p... | mcq | jee-main-2019-online-8th-april-morning-slot | 12,189 |
2zRpE5bM3prv0h6pd33rsa0w2w9jwzia0nc | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Water from a tap emerges vertically downwards with an initial speed of 1.0 ms<sup>–1</sup>
. The cross-sectional area of
the tap is 10<sup>–4</sup> m<sup>2</sup>. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below th... | [{"identifier": "A", "content": "5 \u00d7 10<sup>\u20134</sup> m<sup>2</sup>"}, {"identifier": "B", "content": "2 \u00d7 10<sup>\u20135</sup> m<sup>2</sup>"}, {"identifier": "C", "content": "5 \u00d7 10<sup>\u20135</sup> m<sup>2</sup>"}, {"identifier": "D", "content": "1 \u00d7 10<sup>\u20135</sup> m<sup>2</sup>"}] | ["C"] | null | Using Bernoullie’s equation $${v_2} = \sqrt {v_1^2 + 2gh} $$<br><br>
Equation of continuity<br>
A<sub>1</sub>V<sub>1</sub> = A<sub>2</sub>V<sub>2</sub><br><br>
(1 cm<sup>3</sup>)(1m/s) = $$\left( {{A_2}} \right)\left( {\sqrt {{{\left( 1 \right)}^2} + 2 \times 10 \times {{15} \over {100}}} } \right)$$<br><br>
$$ \Righta... | mcq | jee-main-2019-online-10th-april-evening-slot | 12,190 |
V1d70uFZ8ROvCIn9CQ3rsa0w2w9jx7g9mqj | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | A solid sphere, of radius R acquires a terminal velocity v<sub>1</sub> when falling (due to gravity) through a viscous
fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these
spheres acquires a terminal velocity, v<sub>2</sub>, when falling through the same fluid... | [{"identifier": "A", "content": "$${1 \\over 9}$$"}, {"identifier": "B", "content": "$${1 \\over {27}}$$"}, {"identifier": "C", "content": "27"}, {"identifier": "D", "content": "9"}] | ["D"] | null | $${4 \over 3}$$$$\pi $$R<sup>3</sup> = 27 $$ \times $$ $${4 \over 3}$$$$\pi $$r<sup>3</sup>
<br>$$ \Rightarrow $$ r = $${R \over 3}$$
<br><br>Terminal velocity, $${V_T} = {2 \over 9}{{{r^2}} \over \eta }\left( {{\sigma _s} - {\rho _l}} \right)g$$
<br>$$ \therefore $$ V<sub>T</sub> $$ \propto $$ r<sup>2</sup>
<br><br>$$... | mcq | jee-main-2019-online-12th-april-evening-slot | 12,191 |
DxIhix4LSp1PKXvWhOjgy2xukev0gy2l | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | A cylindrical vessel containing a liquid is
rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of
vessel is 5 cm and the angular speed of
rotation is $$\omega $$ rad s<sup>–1</sup>. The difference in the
height, h (in cm) of liquid at the centre of
vessel and at the side wil... | [{"identifier": "A", "content": "$${{2{\\omega ^2}} \\over {25g}}$$"}, {"identifier": "B", "content": "$${{5{\\omega ^2}} \\over {2g}}$$"}, {"identifier": "C", "content": "$${{25{\\omega ^2}} \\over {2g}}$$"}, {"identifier": "D", "content": "$${{2{\\omega ^2}} \\over {5g}}$$"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265185/exam_images/bfumdyjgh9osnnjfypi6.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 2nd September Morning Slot Physics - Properties of Matter Question 180 English Explanation">
<br><... | mcq | jee-main-2020-online-2nd-september-morning-slot | 12,192 |
Qu6TMjO4cpKn4QSDdNjgy2xukg0bwhjs | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | A fluid is flowing through a horizontal pipe of varying cross-section, with<br/> speed v ms<sup>–1</sup> at a point
where the pressure is P pascal. At another point where pressure is $${P \over 2}$$
Pascal its speed is V ms<sup>–1</sup>. If
the density of the fluid is $$\rho $$ kg m<sup>–3</sup> and the flow is stream... | [{"identifier": "A", "content": "$$\\sqrt {{P \\over {2\\rho }} + {v^2}} $$"}, {"identifier": "B", "content": "$$\\sqrt {{P \\over \\rho } + {v^2}} $$"}, {"identifier": "C", "content": "$$\\sqrt {{{2P} \\over \\rho } + {v^2}} $$"}, {"identifier": "D", "content": "$$\\sqrt {{P \\over \\rho } + {v}} $$"}] | ["B"] | null | From Bernoulli's equation,
<br><br>P + $${1 \over 2}\rho {v^2}$$ = $${P \over 2} + {1 \over 2}\rho {V^2}$$
<br><br>$$ \Rightarrow $$ V = $$\sqrt {{P \over \rho } + {v^2}} $$ | mcq | jee-main-2020-online-6th-september-evening-slot | 12,193 |
eBVwJxHh1HpMhfPbOXjgy2xukfl4r23l | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | In an experiment to verify Stokes law, a small
spherical ball of radius r and density $$\rho $$ falls
under gravity through a distance h in air before
entering a tank of water. If the terminal velocity
of the ball inside water is same as its velocity
just before entering the water surface, then the
value of h is propor... | [{"identifier": "A", "content": "r"}, {"identifier": "B", "content": "r<sup>4</sup>"}, {"identifier": "C", "content": "r<sup>3</sup>"}, {"identifier": "D", "content": "r<sup>2</sup>"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263679/exam_images/oluz76dlbpywqelovbxb.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 5th September Evening Slot Physics - Properties of Matter Question 170 English Explanation">
<br><... | mcq | jee-main-2020-online-5th-september-evening-slot | 12,194 |
pFf55H5aTHZtf74zJ1jgy2xukfambwaa | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density
d. The area of the base of both vessels is S but the height of liquid in one vessel is x<sub>1</sub>
and in the
other, x<sub>2</sub>
. When both cylinders are connected through a pipe of negligible volume very close to... | [{"identifier": "A", "content": "gdS(x<sub>2</sub> + x<sub>1</sub>)<sup>2</sup>"}, {"identifier": "B", "content": "gdS$$\\left( {x_2^2 + x_1^2} \\right)$$"}, {"identifier": "C", "content": "$${1 \\over 4}gdS{\\left( {{x_2} - {x_1}} \\right)^2}$$"}, {"identifier": "D", "content": "$${3 \\over 4}gdS{\\left( {{x_2} - {x_1... | ["C"] | null | $${u_i} = \left[ {dS{x_1}.{{{x_1}} \over 2} + dS{x_2}.{{{x_2}} \over 2}} \right]g\left\{ {dS{x_1} \to m,\,{{{x_1}} \over 2} \to h(C.O.M)} \right\}$$
<br><br>Here total volume remains same.
<br><br>$$ \therefore $$ V<sub>i</sub> = V<sub>f</sub>
<br><br>$$ \Rightarrow $$ S(x<sub>1</sub> + x<sub>2</sub>) = S(h + h)
<br><b... | mcq | jee-main-2020-online-4th-september-evening-slot | 12,195 |
nVfXdosI464ErbTnj17k9k2k5f810o1 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and
minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum
and the maximum velocities of fluid in this pipe is :
| [{"identifier": "A", "content": "$${3 \\over 4}$$"}, {"identifier": "B", "content": "$${9 \\over {16}}$$"}, {"identifier": "C", "content": "$${{\\sqrt 3 } \\over 2}$$"}, {"identifier": "D", "content": "$${{81} \\over {256}}$$"}] | ["B"] | null | Using equation of continuity
<br><br>A<sub>1</sub>V<sub>1</sub>
= A<sub>2</sub>V<sub>2</sub>
<br><br>$$ \Rightarrow $$ $${{{V_1}} \over {{V_2}}} = {{{A_2}} \over {{A_1}}}$$ = $${\left( {{{4.8} \over {6.4}}} \right)^2}$$ = $${9 \over {16}}$$ | mcq | jee-main-2020-online-7th-january-evening-slot | 12,197 |
Cpsh7fqMj5qcaIUJqN1kmioeu2t | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10<sup>$$-$$3</sup> Pa s, respectively. (Density of water : 10<sup>3</sup> kg/m<sup>3</sup>) | [{"identifier": "A", "content": "Steady flow to unsteady flow"}, {"identifier": "B", "content": "Unsteady to steady flow"}, {"identifier": "C", "content": "Remains turbulent flow"}, {"identifier": "D", "content": "Remains steady flow"}] | ["A"] | null | The nature of flow is determined by reynolds no
<br><br>$$R = {{\rho VD} \over \eta }$$
<br><br>If R < 1000 $$ \to $$ flow is steady
<br><br>1000 < R < 2000 $$ \to $$ flow becomes unsteady
<br><br>R > 2000 $$ \to $$ flow is turbulent
<br><br>$${R_1} = {{4 \times {{10}^3} \times 0.18 \times {{10}^{ - 3}}} \... | mcq | jee-main-2021-online-16th-march-evening-shift | 12,198 |
AdVxMyXjmWgWbeHlVF1kmlwsnez | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m<sup>2</sup>. The tank has an opening B near the bottom whose cross-section area is 1 cm<sup>2</sup>. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water com... | [] | null | 3 | <picture><source media="(max-width: 1219px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265493/exam_images/j5lp1ycq7ill54qglbd5.webp"><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263389/exam_images/gjvaedtcfa7hgdpnnqmk.webp"><source media="(max-wi... | integer | jee-main-2021-online-18th-march-evening-shift | 12,199 |
1ks1ayvw3 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum range is ________ m. | [] | null | 6 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265094/exam_images/swuggesnnoapoaz7kzis.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 27th July Evening Shift Physics - Properties of Matter Question 144 English Explanation"><br>$$R =... | integer | jee-main-2021-online-27th-july-evening-shift | 12,201 |
1kte6glqk | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10<sup>$$-$$5</sup> m and density 1.2 $$\times$$ 10<sup>3</sup> kgm<sup>$$-$$3</sup> ? Take viscosity of liquid = 1.8 $$\times$$ 10<sup>$$-$$5</sup> Nsm<sup>$$-$$2</sup>. (Neglect buoyancy due to air). | [{"identifier": "A", "content": "3.8 $$\\times$$ 10<sup>$$-$$11</sup> N"}, {"identifier": "B", "content": "3.9 $$\\times$$ 10<sup>$$-$$10</sup> N"}, {"identifier": "C", "content": "1.8 $$\\times$$ 10<sup>$$-$$10</sup> N"}, {"identifier": "D", "content": "5.8 $$\\times$$ 10<sup>$$-$$10</sup> N"}] | ["B"] | null | Viscous force = Weight<br><br>$$ = \rho \times \left( {{4 \over 3}\pi {r^3}} \right)g$$<br><br>= 3.9 $$\times$$ 10<sup>$$-$$10</sup> | mcq | jee-main-2021-online-27th-august-morning-shift | 12,202 |
1l547dzjv | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs<sup>$$-$$1</sup> and at a speed of 10 ms<sup>$$-$$1</sup>. Then, the initial acceleration of the block, in ms<sup>$$-$$2</sup>, will be :</p>
<p><img src="data:image/png;ba... | [{"identifier": "A", "content": "3"}, {"identifier": "B", "content": "6"}, {"identifier": "C", "content": "5"}, {"identifier": "D", "content": "4"}] | ["C"] | null | <p>F = $$\rho$$ v<sup>2</sup>a</p>
<p>$$\Rightarrow$$ 10 $$\times$$ 1 = 2 $$\times$$ acceleration</p>
<p>$$\Rightarrow$$ Acc. = 5 m/s<sup>2</sup></p> | mcq | jee-main-2022-online-29th-june-morning-shift | 12,203 |
1l54vm24w | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity |
<p>A small spherical ball of radius 0.1 mm and density 10<sup>4</sup> kg m<sup>$$-$$3</sup> falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value... | [] | null | 20 | <p>$$\sqrt {2gh} $$ = terminal speed</p>
<p>$$ \Rightarrow \sqrt {2gh} = {2 \over 9}{{{r^2}g(\rho - \rho ')} \over \eta }$$</p>
<p>$$ = {2 \over 9} \times {{{{10}^{ - 8}} \times 10 \times 9000} \over {{{10}^{ - 5}}}}$$</p>
<p>$$ \Rightarrow h = {{400} \over {2g}}$$</p>
<p>$$ \Rightarrow h = 20$$ m</p> | integer | jee-main-2022-online-29th-june-evening-shift | 12,204 |
1l55jyzkp | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A water drop of radius 1 $$\mu$$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 $$\times$$ 10<sup>$$-$$5</sup> Nsm<sup>$$-$$2</sup> and its density is negligible as compared to that of water 10<sup>6</sup> gm<sup>$$-$$3</sup>. Terminal velocity of the w... | [{"identifier": "A", "content": "145.4 $$\\times$$ 10<sup>$$-$$6</sup> ms<sup>$$-$$1</sup>"}, {"identifier": "B", "content": "118.0 $$\\times$$ 10<sup>$$-$$6</sup> ms<sup>$$-$$1</sup>"}, {"identifier": "C", "content": "132.6 $$\\times$$ 10<sup>$$-$$6</sup> ms<sup>$$-$$1</sup>"}, {"identifier": "D", "content": "123.4 $$... | ["D"] | null | <p>$$6\pi \eta rv = mg$$</p>
<p>$$6\pi \eta rv = {4 \over 3}\pi {r^3}\rho g$$</p>
<p>or $$v = {2 \over 9}{{\rho {r^2}g} \over \eta } = {2 \over 9} \times {{{{10}^3} \times {{({{10}^{ - 6}})}^2} \times 10} \over {1.8 \times {{10}^{ - 5}}}}$$</p>
<p>$$ = 123.4 \times {10^{ - 6}}$$ m/s</p> | mcq | jee-main-2022-online-28th-june-evening-shift | 12,205 |
1l55mdpo5 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A liquid of density 750 kgm<sup>$$-$$3</sup> flows smoothly through a horizontal pipe that tapers in cross-sectional area from A<sub>1</sub> = 1.2 $$\times$$ 10<sup>$$-$$2</sup> m<sup>2</sup> to A<sub>2</sub> = $${{{A_1}} \over 2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa... | [] | null | 24 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5hwlvpk/e1dc1433-e301-4a08-85d1-5de132771340/8a835b90-01bb-11ed-85a8-43d162d2b7e8/file-1l5hwlvpl.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5hwlvpk/e1dc1433-e301-4a08-85d1-5de132771340/8a835b90-01bb-11ed-85a8-43d162d2b7e8... | integer | jee-main-2022-online-28th-june-evening-shift | 12,206 |
1l568efpf | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.</p>
<p>Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.</p>
<p>Reason R : Coefficient of viscosity = $${{Force} \over {Velocity\,gradient}}$$</p>
<p>Cho... | [{"identifier": "A", "content": "Both A and R are true, and R is the correct explanation of A."}, {"identifier": "B", "content": "Both A and R are true but R is NOT the correct explanation of A."}, {"identifier": "C", "content": "A is true but R is false."}, {"identifier": "D", "content": "A is false but R is true."}] | ["C"] | null | <p>[Pressure][Time] = $$\left[ {{{Force} \over {Area}}} \right]$$$$\left[ {{{distance} \over {Area}}} \right]$$</p>
<p>[Coefficient of viscosity] = $$\left[ {{{Force} \over {Area}}} \right]$$$$\left[ {{{distance} \over {Area}}} \right]$$</p>
<p>Statement 'A' is true</p>
<p>But Statement 'R' is false are coefficient of ... | mcq | jee-main-2022-online-28th-june-morning-shift | 12,207 |
1l56ufwdj | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :</p> | [{"identifier": "A", "content": "19.6 m"}, {"identifier": "B", "content": "29.4 m"}, {"identifier": "C", "content": "39.2 m"}, {"identifier": "D", "content": "73.5 m"}] | ["B"] | null | <p>$${t_1} = \sqrt {{{2h} \over g}} $$</p>
<p>$$ = \sqrt {{{2 \times 4.9} \over {9.8}}} = 1\,s$$</p>
<p>$$\Delta t = 4 - 1 = 3\,s$$,</p>
<p>$$v = \sqrt {2gh} = \sqrt {2 \times 9.8 \times 4.9} = 9.8$$ m/s</p>
<p>$$\therefore$$ depth $$ = 9.8 \times 3 = 29.4$$ m</p> | mcq | jee-main-2022-online-27th-june-evening-shift | 12,208 |
1l57pxfvm | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The velocity of a small ball of mass 'm' and density d<sub>1</sub>, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d<sub>2</sub>, then the viscous force acting on the ball, will be :</p> | [{"identifier": "A", "content": "$$mg\\left( {1 - {{{d_1}} \\over {{d_2}}}} \\right)$$"}, {"identifier": "B", "content": "$$mg\\left( {1 - {{{d_2}} \\over {{d_1}}}} \\right)$$"}, {"identifier": "C", "content": "$$mg\\left( {{{{d_1}} \\over {{d_2}}} - 1} \\right)$$"}, {"identifier": "D", "content": "$$mg\\left( {{{{d_2}... | ["B"] | null | <p>Viscous force acting on the ball will be equal and opposite to net of weight and buoyant force</p>
<p>$$ \Rightarrow {F_0} = {4 \over 3}\pi {r^3}{d_1}g - {4 \over 3}\pi {r^3}{d_2}g$$</p>
<p>$$ = {4 \over 3}\pi {r^3}{d_1}g\left( {1 - {{{d_2}} \over {{d_1}}}} \right)$$</p>
<p>$$ = mg\left( {1 - {{{d_2}} \over {{d_1}}}... | mcq | jee-main-2022-online-27th-june-morning-shift | 12,209 |
1l57qy8zv | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The area of cross-section of a large tank is 0.5 m<sup>2</sup>. It has a narrow opening near the bottom having area of cross-section 1 cm<sup>2</sup>. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at th... | [] | null | 300 | <p>By Bernoulli's theorem:</p>
<p>$${{250} \over {0.5}} + \rho gh = {1 \over 2}\rho {v^2}$$</p>
<p>$$\Rightarrow$$ v = 3 m/s</p>
<p>$$\Rightarrow$$ v = 300 cm/s</p> | integer | jee-main-2022-online-27th-june-morning-shift | 12,210 |
1l58d85zm | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>An ideal fluid of density 800 kgm<sup>$$-$$3</sup>, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $${a \over 2}$$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $${{\sqrt x } \over 6}... | [] | null | 363 | <p>From Bernoulli's equation</p>
<p>$${P_1} + {1 \over 2}\rho {v_1}^2 + \rho g{h_1} = {P_2} + {1 \over 2}\rho {v_2}^2 + \rho g{h_2}$$</p>
<p>$${P_1} - {P_2} + \rho g({h_1} - {h_2}) = {1 \over 2}\rho ({v_2}^2 - {v_1}^2)$$ ...... (i)</p>
<p>Also, from equation of continuity</p>
<p>$${A_1}{v_1} = {A_2}{v_2}$$</p>
<p>$$A{v... | integer | jee-main-2022-online-26th-june-morning-shift | 12,211 |
1l58hmu8q | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R<sub>e</sub> is :</p> | [{"identifier": "A", "content": "$${R_e} = {{\\eta d} \\over {\\rho v}}$$"}, {"identifier": "B", "content": "$${R_e} = {{\\rho v} \\over {\\eta d}}$$"}, {"identifier": "C", "content": "$${R_e} = {{\\rho vd} \\over \\eta }$$"}, {"identifier": "D", "content": "$${R_e} = {\\eta \\over {\\rho vd}}$$"}] | ["C"] | null | <p>The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict the onset of turbulence. It is defined as:</p>
<p>$$Re = \frac{{\rho v d}}{{\eta}}$$</p>
<p>where:</p>
<ul>
<li>$\rho$ is the fluid density</li>
<li>$v$ is the fluid velocity</li>
<li>$d$ is a characteristic linear dimension (for... | mcq | jee-main-2022-online-26th-june-evening-shift | 12,212 |
1l5akad4b | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The terminal velocity (v<sub>t</sub>) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :</p> | [{"identifier": "A", "content": "r<sup>1/2</sup>"}, {"identifier": "B", "content": "r"}, {"identifier": "C", "content": "r<sup>2</sup>"}, {"identifier": "D", "content": "r<sup>3</sup>"}] | ["C"] | null | <p>$$6\pi \eta {v_t}r = {4 \over 3}\pi {r^3}(\rho - \sigma )g$$</p>
<p>$$ \Rightarrow {v_t} = C{r^2}$$ where C is a constant</p>
<p>or $${v_t} \propto {r^2}$$</p> | mcq | jee-main-2022-online-25th-june-morning-shift | 12,213 |
1l5al9xtr | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The velocity of upper layer of water in a river is 36 kmh<sup>$$-$$1</sup>. Shearing stress between horizontal layers of water is 10<sup>$$-$$3</sup> Nm<sup>$$-$$2</sup>. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10<sup>$$-$$2</sup> Pa.s)</p> | [] | null | 100 | <p>$$F = - \eta A{{du} \over {dx}}$$</p>
<p>$$ \Rightarrow {10^{ - 3}} = {10^{ - 2}} \times {{10} \over h}$$</p>
<p>$$ \Rightarrow h = {{{{10}^{ - 1}}} \over {{{10}^{ - 3}}}}$$ m = 100 m</p>
<p>$$\Rightarrow$$ (100)</p> | integer | jee-main-2022-online-25th-june-morning-shift | 12,214 |
1l5w210bb | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>An air bubble of negligible weight having radius r rises steadily through a solution of density $$\sigma$$ at speed v. The coefficient of viscosity of the solution is given by :</p> | [{"identifier": "A", "content": "$$\\eta = {{4r\\sigma g} \\over {9v}}$$"}, {"identifier": "B", "content": "$$\\eta = {{2{r^2}\\sigma g} \\over {9v}}$$"}, {"identifier": "C", "content": "$$\\eta = {{2\\pi {r^2}\\sigma g} \\over {9v}}$$"}, {"identifier": "D", "content": "$$\\eta = {{2{r^2}\\sigma g} \\over {3\\pi v}... | ["B"] | null | <p>Air bubble moves with constant speed v. So net force = 0.</p>
<p>$$\therefore$$ Buoyant Force = Viscous force</p>
<p>$$ \Rightarrow {F_b} = {F_v}$$</p>
<p>$$ \Rightarrow \sigma \times {4 \over 3}\pi {r^3}g = 6\pi nrv$$</p>
<p>$$ \Rightarrow n = {{2\sigma {r^2}g} \over {9v}}$$</p> | mcq | jee-main-2022-online-30th-june-morning-shift | 12,215 |
1l6m9r89x | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A balloon has mass of $$10 \mathrm{~g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5 \mathrm{~cm} / \mathrm{s}$$. If the balloon shrinks in $$5 \mathrm{~s}$$ completely. Then, the average force acting on that balloon will be (in dyne).</p> | [{"identifier": "A", "content": "3"}, {"identifier": "B", "content": "9"}, {"identifier": "C", "content": "12"}, {"identifier": "D", "content": "18"}] | ["B"] | null | <p>$${F_{avg}} = \mu \times {v_{rel}}$$</p>
<p>$$ = {{10} \over 5} \times 4.5 = 9$$</p> | mcq | jee-main-2022-online-28th-july-morning-shift | 12,216 |
1l6mbmjvc | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The diameter of an air bubble which was initially $$2 \mathrm{~mm}$$, rises steadily through a solution of density $$1750 \mathrm{~kg} \mathrm{~m}^{-3}$$ at the rate of $$0.35 \,\mathrm{cms}^{-1}$$. The coefficient of viscosity of the solution is _________ poise (in nearest integer). (the density of air is negligibl... | [] | null | 11 | <p>$$F = 6\pi \eta rv$$</p>
<p>$${4 \over 3}\pi {r^3}{\rho _l}g = 6\pi \eta rv$$</p>
<p>$$\eta = {{2{r^2}{\rho _l}g} \over v}$$</p>
<p>$$ = {{2 \times {{(2 \times {{10}^{ - 3}})}^2} \times 1750 \times 10} \over {9 \times 3.5 \times {{10}^{ - 3}} \times 4}}$$</p>
<p>$$ = 11$$ poise</p> | integer | jee-main-2022-online-28th-july-morning-shift | 12,217 |
1l6nrfi2b | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Consider a cylindrical tank of radius $$1 \mathrm{~m}$$ is filled with water. The top surface of water is at $$15 \mathrm{~m}$$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $$5 \mathrm{~m}$$ from the bottom. A force of $$5 \times 10^{5} \mathrm{~N}$$ is applied an the top s... | [{"identifier": "A", "content": "11.6 m/s"}, {"identifier": "B", "content": "10.8 m/s"}, {"identifier": "C", "content": "17.8 m/s"}, {"identifier": "D", "content": "14.4 m/s"}] | ["C"] | null | <p>By Bernoulli's theorem,</p>
<p>$${{5 \times {{10}^5}} \over {\pi {{(1)}^2}}} + \rho g(10) = 1.01 \times {10^5} + {1 \over 2}\rho {(v)^2}$$</p>
<p>$$ \Rightarrow {v^2} = 200 + {{{{10}^6}} \over {1000\pi }} - 202$$</p>
<p>$$ \Rightarrow v \simeq 17.8$$ m/s</p> | mcq | jee-main-2022-online-28th-july-evening-shift | 12,218 |
1ldnzb3qt | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The surface of water in a water tank of cross section area $$750 \mathrm{~cm}^{2}$$ on the top of a house is $$h \mathrm{~m}$$ above the tap level. The speed of water coming out through the tap of cross section area $$500 \mathrm{~mm}^{2}$$ is $$30 \mathrm{~cm} / \mathrm{s}$$. At that instant, $$\frac{d h}{d t}$$ is... | [] | null | 2 | $\begin{aligned} & \mathrm{AV}=\mathrm{av} \\\\ & 750 \times 10^{-4} \times\left(\frac{d h}{d t}\right)=\left(500 \times 10^{-6}\right)\left(30 \times 10^{-2}\right) \\\\ & \frac{d h}{d t}=\frac{15 \times 10^{-5}}{75 \times 10^{-3}} \\\\ & =\frac{1}{5} \times 10^{-2} \\\\ & =2 \times 10^{-3} \mathrm{~m} / \mathrm{s} \\... | integer | jee-main-2023-online-1st-february-evening-shift | 12,219 |
1ldsaqrqk | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A fully loaded boeing aircraft has a mass of $$5.4\times10^5$$ kg. Its total wing area is 500 m$$^2$$. It is in level flight with a speed of 1080 km/h. If the density of air $$\rho$$ is 1.2 kg m$$^{-3}$$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface ... | [{"identifier": "A", "content": "16"}, {"identifier": "B", "content": "8"}, {"identifier": "C", "content": "6"}, {"identifier": "D", "content": "10"}] | ["D"] | null | <p>Velocity of aircraft = 1050 km/h = 300 m/s</p>
<p>Now, weight of aircraft = $$\Delta PA$$</p>
<p>$$\Delta P = {{5.4 \times {{10}^5} \times g} \over {500}} = 10800$$ $$\mathrm{Pa}$$</p>
<p>From Bernoulli's principle</p>
<p>$$\Delta P = {1 \over 2}\rho \left[ {V_{upper}^2 - V_{lower}^2} \right]$$</p>
<p>$$10800 = {1 \... | mcq | jee-main-2023-online-29th-january-evening-shift | 12,220 |
1ldsbn7vf | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A metal block of base area 0.20 m$$^2$$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. IF the viscosity of the liquid is $$5.0\times10^{-3}~\mathrm{Pl}$$, the... | [] | null | 25 | <p>As the block moves with constant speed, the horizontal force is balanced by viscous force thus</p>
<p>$$F = \eta A{{\Delta v} \over {\Delta z}}$$</p>
<p>$$0.1 = 5 \times {10^{ - 3}} \times 0.2 \times {v \over {.25 \times {{10}^{ - 3}}}}$$</p>
<p>$$ \Rightarrow v = 25 \times {10^{ - 3}}$$ m/s</p> | integer | jee-main-2023-online-29th-january-evening-shift | 12,221 |
1ldws8rkz | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $$3696\times10^{-x}$$ N. The value of $$x$$ is ________.
<br/><br/>
(Given, g = 9.8 m/s$$^2$$ and $$\pi=\frac{22}{7}$... | [] | null | 7 | <p>At state of terminal speed, net force on the ball is zero</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le4brdey/5c2eabeb-ef73-4434-b43d-e1a90477c1a2/c57da0a0-ac71-11ed-b877-bf6a71b74f80/file-1le4brdez.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le4brdey/5c2eabeb... | integer | jee-main-2023-online-24th-january-evening-shift | 12,222 |
1lgozs7t5 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$</p>
<p>Assertion A : A spherical body of radius $$(5 \pm 0.1) \mathrm{mm}$$ having a particular density is falling through a liquid of constant density. The percentage error in the calculati... | [{"identifier": "A", "content": "A is false but $$\\mathbf{R}$$ is true"}, {"identifier": "B", "content": "$$\\mathrm{A}$$ is true but $$\\mathbf{R}$$ is false"}, {"identifier": "C", "content": "Both $$\\mathbf{A}$$ and $$\\mathbf{R}$$ are true but $$\\mathbf{R}$$ is NOT the correct explanation of $$\\mathbf{A}$$"}, {"... | ["B"] | null | <p>The terminal velocity $$v_t$$ of a spherical body falling through a viscous fluid is given by Stokes' Law, which states that:</p>
$$ v_t = \frac{2}{9}\frac{(\rho_s - \rho_f)gr^2}{\eta} $$
<p>where:</p>
<ul>
<li>$ \rho_s $ is the density of the sphere</li>
<li>$ \rho_f $ is the density of the fluid</li>
<... | mcq | jee-main-2023-online-13th-april-evening-shift | 12,223 |
1lgvti3ux | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $$2.0 \mathrm{~cm}^{2}$$. The area of cross section at the outlet is $$10 \mathrm{~mm}^{2}$$. If the piston is pushed at a speed of $$4 \mathrm{~cm} \mathrm{~s}^{-1}$$, the speed of outgoing fluid is __________ $$\mathr... | [] | null | 80 | By equation of continuity
<br/><br/>$$
\begin{aligned}
& \mathrm{A}_1 \mathrm{~V}_1=\mathrm{A}_2 \mathrm{~V}_2 \\\\
& \mathrm{~V}_2=\frac{2 \times 4}{10 \times 10^{-2}}=80 \mathrm{~cm} / \mathrm{s}
\end{aligned}
$$ | integer | jee-main-2023-online-10th-april-evening-shift | 12,224 |
1lh24geed | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A small ball of mass $$\mathrm{M}$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_{0}$$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?</p> | [{"identifier": "A", "content": "$$\\mathrm{F}=\\mathrm{Mg}\\left(1-\\frac{\\rho_{\\mathrm{O}}}{\\rho}\\right)$$"}, {"identifier": "B", "content": "$$\\mathrm{F}=\\mathrm{Mg}\\left(1+\\frac{\\rho}{P_{o}}\\right)$$"}, {"identifier": "C", "content": "$$\\mathrm{F}=\\mathrm{Mg}\\left(1+\\frac{\\rho_{\\mathrm{o}}}{\\rho}\\... | ["A"] | null | <p>When the ball is falling with a constant velocity, it means the net force acting on the ball is zero. This is because it's in a state of dynamic equilibrium - the downward force equals the upward force.</p>
<p>The downward force is the gravitational force (weight of the ball), which is given by $F_g = Mg$.</p>
<... | mcq | jee-main-2023-online-6th-april-morning-shift | 12,226 |
lsblgcp1 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is ___________ kg.<br/><br/> (Take air d... | [] | null | 9600 | <p>To solve this problem, we need to employ Bernoulli's equation, which is applied to describe the behavior of fluid flow. For a fluid in steady flow, the principle states that the sum of the pressure potential energy density, kinetic energy density, and the gravitational potential energy density has the same value at ... | integer | jee-main-2024-online-1st-february-morning-shift | 12,227 |
jaoe38c1lscq3vvz | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>The reading of pressure metre attached with a closed pipe is $$4.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2$$. On opening the valve, water starts flowing and the reading of pressure metre falls to $$2.0 \times 10^4 \mathrm{~N} / \mathrm{m}^2$$. The velocity of water is found to be $$\sqrt{V} \mathrm{~m} / \mathrm{s}$$... | [] | null | 50 | <p>$$\begin{aligned}
& \text { Change in pressure }=\frac{1}{2} \rho \mathrm{v}^2 \\
& 4.5 \times 10^4-2.0 \times 10^4=\frac{1}{2} \times 10^3 \times \mathrm{v}^2 \\
& 2.5 \times 10^4=\frac{1}{2} \times 10^3 \times \mathrm{v}^2 \\
& \mathrm{v}^2=50 \\
& \mathrm{v}=\sqrt{50} \\
& \text { Velocity of water }=\sqrt{\mathr... | integer | jee-main-2024-online-27th-january-evening-shift | 12,228 |
jaoe38c1lsd68gpq | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A small spherical ball of radius $$r$$, falling through a viscous medium of negligible density has terminal velocity '$$v$$'. Another ball of the same mass but of radius $$2 r$$, falling through the same viscous medium will have terminal velocity:</p> | [{"identifier": "A", "content": "$$4 \\mathrm{v}$$\n"}, {"identifier": "B", "content": "$$2 \\mathrm{~V}$$\n"}, {"identifier": "C", "content": "$$\\frac{v}{4}$$\n"}, {"identifier": "D", "content": "$$\\frac{\\mathrm{v}}{2}$$"}] | ["D"] | null | <p>Since density is negligible hence Buoyancy force will be negligible</p>
<p>At terminal velocity.</p>
<p>$$\mathrm{Mg} =6 \pi \eta \mathrm{rv}$$</p>
<p>$$\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad$$ (as mass is constant)</p>
<p>Now, $$\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$$... | mcq | jee-main-2024-online-31st-january-evening-shift | 12,229 |
jaoe38c1lse6knig | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?</p> | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsegk5m8/fe78d00f-024b-49c9-8f0d-067457052cd5/683f8e10-c72f-11ee-8cb5-7deab4010c9e/file-6y3zli1lsegk5m9.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/6y3zli1lsegk5m8/fe78d00f-024b-49c9-8f0... | ["B"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lslua86l/cc70e2fa-7aa3-4caf-91b3-a69911e05e09/907dd2c0-cb3e-11ee-ad47-a16d1086e690/file-6y3zli1lslua86m.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lslua86l/cc70e2fa-7aa3-4caf-91b3-a69911e05e09/907dd2c0-cb3e-11ee... | mcq | jee-main-2024-online-31st-january-morning-shift | 12,230 |
jaoe38c1lsf2deu8 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $$70 \mathrm{~ms}^{-1}$$ and $$65 \mathrm{~ms}^{-1}$$ respectively. If the wing area is $$2 \mathrm{~m}^2$$, the lift of the wing is _________ $$N$$.</p>
<p>(Given density of air $$=1.2 \mathrm{... | [] | null | 810 | <p>$$\begin{aligned}
& \mathrm{F}=\frac{1}{2} \rho\left(\mathrm{v}_1^2-\mathrm{v}_2^2\right) \mathrm{A} \\
& \mathrm{F}=\frac{1}{2} \times 1.2 \times\left(70^2-65^2\right) \times 2 \\
& =810 \mathrm{~N}
\end{aligned}$$</p> | integer | jee-main-2024-online-29th-january-morning-shift | 12,231 |
luxwderb | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A spherical ball of radius $$1 \times 10^{-4} \mathrm{~m}$$ and density $$10^5 \mathrm{~kg} / \mathrm{m}^3$$ falls freely under gravity through a distance $$h$$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $$h$$ is approximately:</p>
<p>(The ... | [{"identifier": "A", "content": "2518 m"}, {"identifier": "B", "content": "2396 m"}, {"identifier": "C", "content": "2249 m"}, {"identifier": "D", "content": "2296 m"}] | ["A"] | null | <p>To solve this problem, we can use the concepts of terminal velocity and the forces acting on the spherical ball. First, let's analyze the situation step-by-step.</p>
<p>When the ball falls freely under gravity, it achieves a terminal velocity $$v_t$$ in water. This terminal velocity is reached when the gravitationa... | mcq | jee-main-2024-online-9th-april-evening-shift | 12,232 |
lv3vefl7 | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Small water droplets of radius $$0.01 \mathrm{~mm}$$ are formed in the upper atmosphere and falling with a terminal velocity of $$10 \mathrm{~cm} / \mathrm{s}$$. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be ________ $$\mathrm{cm} / \mathrm{s}$$.</p... | [] | null | 40 | <p>To find the new terminal velocity of the larger drop formed by the coalescence of 8 smaller droplets, we need to understand the relationship between the radius of the droplets and their terminal velocity.</p>
<p>The terminal velocity for a small spherical droplet falling through the air is given by the Stokes' law:... | integer | jee-main-2024-online-8th-april-evening-shift | 12,234 |
lv5gse1i | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>Correct Bernoulli's equation is (symbols have their usual meaning) :</p> | [{"identifier": "A", "content": "$$P+\\frac{1}{2} \\rho g h+\\frac{1}{2} \\rho v^2=$$ constant\n"}, {"identifier": "B", "content": "$$P+m g h+\\frac{1}{2} m v^2=$$ constant\n"}, {"identifier": "C", "content": "$$P+\\rho g h+\\rho v^2=$$ constant\n"}, {"identifier": "D", "content": "$$P+\\rho g h+\\frac{1}{2} \\rho v^2=... | ["D"] | null | <p>Bernoulli's equation relates the pressure, velocity, and height in a flowing fluid and is derived from the principle of conservation of energy. The correct form of Bernoulli's equation is:</p>
<p>$$P + \rho g h + \frac{1}{2} \rho v^2 = \text{constant}$$</p>
<p>where:</p>
<ul>
<li><b>P</b> is the pressure within ... | mcq | jee-main-2024-online-8th-april-morning-shift | 12,235 |
lvc57nro | physics | properties-of-matter | fluid-flow,-bernoulli's-principle-and-viscosity | <p>A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :</p> | [{"identifier": "A", "content": "$$m g\\left(1-\\frac{\\rho_0}{\\rho}\\right)$$\n"}, {"identifier": "B", "content": "$$m g\\left(\\frac{\\rho_0}{\\rho}-1\\right)$$\n"}, {"identifier": "C", "content": "$$m g\\left(1-\\rho \\rho_0\\right)$$\n"}, {"identifier": "D", "content": "$$m g\\left(1+\\frac{\\rho}{\\rho_0}\\right)... | ["A"] | null | <p>$$\begin{aligned}
& F_V=\left(m g-F_B\right) \frac{m g}{m g}=\left(\frac{\rho V_g-\rho_0 V_g}{\rho V_g}\right) m g \\
& F_v=m g\left(1-\frac{\rho_0}{\rho}\right)
\end{aligned}$$</p> | mcq | jee-main-2024-online-6th-april-morning-shift | 12,236 |
RiPAAa5xJCjViIwD | physics | properties-of-matter | mechanical-properties-of-solids | A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is | [{"identifier": "A", "content": "$$2Fl$$ "}, {"identifier": "B", "content": "$$Fl$$ "}, {"identifier": "C", "content": "$${F \\over {2l}}$$ "}, {"identifier": "D", "content": "$${{Fl} \\over 2}$$ "}] | ["D"] | null | Work done by constant force in displacing the object by a distance $$\ell $$.
<br><br>= Potential energy stored
<br><br>$$ = {1 \over 2} \times $$ Stress $$ \times $$ Strain $$ \times $$ Volume
<br><br>$$ = {1 \over 2} \times {F \over A} \times {l \over L} \times AL$$
<br><br>$$ = {1 \over 2}Fl$$ | mcq | aieee-2004 | 12,237 |
5c7wvUHfFHzyXpmW | physics | properties-of-matter | mechanical-properties-of-solids | A wire elongates by $$l$$ $$mm$$ when a LOAD $$W$$ is hanged from it. If the wire goes over a pulley and two weights $$W$$ each are hung at the two ends, the elongation of the wire will be (in $$mm$$) | [{"identifier": "A", "content": "$$l$$ "}, {"identifier": "B", "content": "$$2l$$ "}, {"identifier": "C", "content": "zero "}, {"identifier": "D", "content": "$$l/2$$ "}] | ["A"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/VziGeT1LnBSiMcIo3/Qf3l58WRI6PIxnzyG1XLssQb5QbCP/SONBvy8aDyvZpp5uY4Wj2Z/image.svg" loading="lazy" alt="AIEEE 2006 Physics - Properties of Matter Question 240 English Explanation">
<br>Case $$(i)$$
<br>At equilibrium, $$T=W$$
<br>$$Y = {{W/A} \over {\ell /... | mcq | aieee-2006 | 12,238 |
4E6505zL8Y7DJqxT | physics | properties-of-matter | mechanical-properties-of-solids | Two wires are made of the same material and have the same volume. However wire $$1$$ has cross-sectional area $$A$$ and wire $$2$$ has cross-sectional area $$3A.$$ If the length of wire $$1$$ increases by $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch wire $$2$$ by the same amount? | [{"identifier": "A", "content": "$$4F$$ "}, {"identifier": "B", "content": "$$6F$$ "}, {"identifier": "C", "content": "$$9F$$"}, {"identifier": "D", "content": "$$F$$ "}] | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/40OoXqkX0j40joIBG/yOPAubVBfaQcyNx7nYBxNjDkguC2f/GWM7lXbHGEd2tBbaFrY2Fb/image.svg" loading="lazy" alt="AIEEE 2009 Physics - Properties of Matter Question 237 English Explanation"> <br>As shown in the figure, the wires will have the same Young's modulus (sa... | mcq | aieee-2009 | 12,239 |
HYPrE568wzdj69p3ZyqSw | physics | properties-of-matter | mechanical-properties-of-solids | A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi $$kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is <b>false</b> ? | [{"identifier": "A", "content": "$${{\\Delta \\gamma } \\over \\gamma }$$ gets minimum contribution\nfrom the uncertainty in the length."}, {"identifier": "B", "content": "The figure of merit is the largest for the length of the rod."}, {"identifier": "C", "content": "The maximum value of $$\\gamma $$ that can be deter... | ["C"] | null | <p>Young's Modulus of the material of the rod is</p>
<p>$$Y = {{Stress} \over {Strain}} = {{(F/A)} \over {(\Delta l/l)}}$$</p>
<p>Here, Y remains maximum, when $$\Delta$$l is of least count.</p>
<p>That is,</p>
<p>$${Y_{\max }} = \left[ {{{50\pi \times {{10}^3}N} \over {\pi {{(5 \times {{10}^{ - 3}})}^2}{m^2}}}} \righ... | mcq | jee-main-2016-online-10th-april-morning-slot | 12,240 |
zdD0wVmKXtdZg2E0Owa42 | physics | properties-of-matter | mechanical-properties-of-solids | A uniformly tapering conical wire is made from a material of Young’s modulus
Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The ... | [{"identifier": "A", "content": "L $$\\left( {1 + {2 \\over 9}{{Mg} \\over {\\pi Y{R^2}}}} \\right)$$"}, {"identifier": "B", "content": "L $$\\left( {1 + {1 \\over 3}{{Mg} \\over {\\pi Y{R^2}}}} \\right)$$"}, {"identifier": "C", "content": "L $$\\left( {1 + {1 \\over 9}{{Mg} \\over {\\pi Y{R^2}}}} \\right)$$"}, {"ident... | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266563/exam_images/vngwoucwip8wkgnt2s55.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2016 (Online) 9th April Morning Slot Physics - Properties of Matter Question 214 English Explanation">
<br><br... | mcq | jee-main-2016-online-9th-april-morning-slot | 12,241 |
5Fr2EmRJzoJz60RU | physics | properties-of-matter | mechanical-properties-of-solids | A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his
density remains same, the stress in the leg will change by a factor of : | [{"identifier": "A", "content": "$${1 \\over {81}}$$"}, {"identifier": "B", "content": "9"}, {"identifier": "C", "content": "$${1 \\over {9}}$$"}, {"identifier": "D", "content": "81"}] | ["B"] | null | <p>To determine how the stress in the leg changes when a man's linear dimensions increase by a factor of 9, we can analyze the relationship between the dimensions and the stress on the legs.</p>
<p>First, let's establish some relationships:
<ol>
<li>Linear dimensions (length, width, height) increase by a factor of 9... | mcq | jee-main-2017-offline | 12,242 |
E1fhHHnC7NNfj8KM | physics | properties-of-matter | mechanical-properties-of-solids | A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a
cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross
section of cylindrical container. When a mass m is placed on the surface of the piston to compress the
liquid,... | [{"identifier": "A", "content": "$${{mg} \\over {Ka}}$$ "}, {"identifier": "B", "content": "$${{Ka} \\over {mg}}$$ "}, {"identifier": "C", "content": "$${{Ka} \\over {3mg}}$$ "}, {"identifier": "D", "content": "$${{mg} \\over {3Ka}}$$ "}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265887/exam_images/af1waeebrqafuq16vn6b.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2018 (Offline) Physics - Properties of Matter Question 222 English Explanation">
<br><br>Because of m mass the... | mcq | jee-main-2018-offline | 12,243 |
m28EdBj1AHoR2SOtEwbSL | physics | properties-of-matter | mechanical-properties-of-solids | As shown in the figure, forces of 10<sup>5</sup> N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement wi... | [{"identifier": "A", "content": "0.25 cm"}, {"identifier": "B", "content": "0.37 cm"}, {"identifier": "C", "content": "0.75 cm"}, {"identifier": "D", "content": "1.00 cm"}] | ["A"] | null | <p>Given : Force applied F = 10<sup>5</sup> N; side of cube x = 10 m = 10 $$\times$$ 10<sup>$$-$$2</sup> m; shift dx = 0.5 cm = 0.5 $$\times$$ = 10<sup>$$-$$2</sup> m</p>
<p> <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l3312yyp/f507ef23-c61a-49fa-89e4-d31c8f1eab71/d9cc8f10-d1f4-11ec-b83f-ebfea68213... | mcq | jee-main-2018-online-15th-april-evening-slot | 12,244 |
u3IuZmrPwS8FDDq1e28y6 | physics | properties-of-matter | mechanical-properties-of-solids | A steel wire having a radius of 2.0 mm,
carrying a load of 4 kg, is hanging from a
ceiling. Given that g = 3.1 p ms<sup>–2</sup>, what will be
the tensile stress that would be developed in the
wire ? | [{"identifier": "A", "content": "3.1 \u00d7 10<sup>6</sup> Nm<sup>\u20132</sup>"}, {"identifier": "B", "content": "6.2 \u00d7 10<sup>6</sup> Nm<sup>\u20132</sup>"}, {"identifier": "C", "content": "4.8 \u00d7 10<sup>6</sup> Nm<sup>\u20132</sup>"}, {"identifier": "D", "content": "5.2 \u00d7 10<sup>6</sup> Nm<sup>\u20132<... | ["A"] | null | Tensile stress in wire will be<br><br>
= $${{Tensile{\rm{ }}force} \over {Cross{\rm{ }}section{\rm{ }}Area}}$$<br><br>
= $${{mg} \over {\pi {R^2}}} = {{4 \times 3.1\pi } \over {\pi \times 4 \times {{10}^{ - 6}}}}N{m^{ - 2}}$$<br><br>
= 3.1 × 10<sup>6</sup> Nm<sup>–2</sup> | mcq | jee-main-2019-online-8th-april-morning-slot | 12,246 |
sfjvWDEF1lrWPk7u3xrf2 | physics | properties-of-matter | mechanical-properties-of-solids | Young's moduli of two wires A and B are in the
ratio 7 : 4. Wire A is 2 m long and has radius R.
Wire B is 1.5 m long and has radius 2 mm. If
the two wires stretch by the same length for a
given load, then the value of R is close to :- | [{"identifier": "A", "content": "1.7 mm"}, {"identifier": "B", "content": "1.9 mm"}, {"identifier": "C", "content": "1.3 mm"}, {"identifier": "D", "content": "1.5 mm"}] | ["A"] | null | Given:<br><br>
$${{{Y_A}} \over {{Y_B}}} = {7 \over 4};\,{L_A} = 2m\,;{A_A} = \pi {R^2}$$<br><br>
$${F \over A} = Y\left( {{l \over L}} \right);{L_B} = 1.5m\,;{A_B} = \pi {(2mm)^2}$$<br><br>
given F and $$l$$ are same $$ \Rightarrow $$ $${{AY} \over L}$$ is same<br><br>
$${{{A_A}{Y_A}} \over {{L_A}}} = {{{A_B}{Y_B}} \... | mcq | jee-main-2019-online-8th-april-evening-slot | 12,247 |
5AuQ1lpbd5dl3vApLN3rsa0w2w9jwzkr8qb | physics | properties-of-matter | mechanical-properties-of-solids | In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm<sup>2</sup>
are used. The
wires are connected in series and one end of the combined wire is connected to a rigid support and other end
is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is,
[Gi... | [{"identifier": "A", "content": "8.0 \u00d7 10<sup>6</sup> N/m<sup>2</sup>"}, {"identifier": "B", "content": "1.2 \u00d7 10<sup>6</sup> N/m<sup>2</sup>"}, {"identifier": "C", "content": "0.2 \u00d7 10<sup>6</sup> N/m<sup>2</sup>"}, {"identifier": "D", "content": "1.8 \u00d7 10<sup>6</sup> N/m<sup>2</sup>"}] | ["A"] | null | Corresponding to the stress ($$\sigma $$)<br><br>
Total elongation $$\Delta {I_{net}} = {{\sigma {L_1}} \over {{Y_1}}} + {{\sigma {L_2}} \over {{Y_2}}}$$<br><br>
$$\sigma = \Delta I\left( {{{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}} \right)$$<br><br>
$$ = 0.2 \times {10^{ - 3}} \times \left( {{{120 \times 60} \over {180}}} ... | mcq | jee-main-2019-online-10th-april-evening-slot | 12,248 |
mc6HbLgr5N2zZ8U0vN3rsa0w2w9jx7ibh2q | physics | properties-of-matter | mechanical-properties-of-solids | A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of
Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net
longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of
the material ... | [{"identifier": "A", "content": "$${{3F} \\over {\\left( {\\pi {r^2}YT} \\right)}}$$"}, {"identifier": "B", "content": "$${{6F} \\over {\\left( {\\pi {r^2}YT} \\right)}}$$"}, {"identifier": "C", "content": "$${F \\over {\\left( {3\\pi {r^2}YT} \\right)}}$$"}, {"identifier": "D", "content": "$${9F\\left( {\\pi {r^2}YT} ... | ["A"] | null | Change in length due to temperature change,
<br><br>$$\Delta $$$$l$$ = $$l$$$$\alpha $$$$\Delta $$T
<br><br>$${{\Delta l} \over l}$$ = $$\alpha $$T [ Here $$\Delta $$T = T ]
<br><br>Y = $${{{F \over {\pi {r^2}}}} \over {{{\Delta l} \over l}}}$$
<br><br> = $${{{F \over {\pi {r^2}}}} \over {\alpha T}}$$
<br><br>$$ \Righ... | mcq | jee-main-2019-online-12th-april-evening-slot | 12,249 |
OhLIURWf5g076tm6fPjgy2xukexyty0n | physics | properties-of-matter | mechanical-properties-of-solids | A wire of density 9 $$ \times $$ 10<sup>–3</sup> kg cm<sup>–3</sup> is stretched
between two clamps 1 m apart. The resulting
strain in the wire is 4.9 $$ \times $$ 10<sup>–4</sup>. The lowest
frequency of the transverse vibrations in the
wire is : (Young’s modulus of wire Y = 9 $$ \times $$ 10<sup>10</sup>
Nm<sup>–2</s... | [] | null | 35 | $$\rho $$<sub>wire</sub> = 9 $$ \times $$ 10<sup>–3</sup> kg cm<sup>–3</sup>
<br><br>= $${{9 \times {{10}^{ - 3}}} \over {{{10}^{ - 6}}}}$$ kg/m<sup>3</sup>
= 9000 kg/m<sup>2</sup>
<br><br>f = $${1 \over {2l}}\sqrt {{T \over \mu }} = $$$${1 \over {2l}}\sqrt {{T \over {{\rho _{wire}}A}}} $$
<br><br>= $${1 \over {2l}}\... | integer | jee-main-2020-online-2nd-september-evening-slot | 12,250 |
QHDq0apaUDoblbX1Z9jgy2xukfajwke5 | physics | properties-of-matter | mechanical-properties-of-solids | A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the
length of the side of the cube is close to :
<br/>(Given bulk modulus of metal, B = 8 $$ \times $$ 10<sup>10</sup> Pa) | [{"identifier": "A", "content": "0.6"}, {"identifier": "B", "content": "20"}, {"identifier": "C", "content": "1.67"}, {"identifier": "D", "content": "5"}] | ["C"] | null | Bulk Modulus, B = $$\left( - \right){{\Delta P} \over {\Delta V/V}} $$<br><br>$$\Delta P = -\left( {{{\Delta V} \over V}} \right).B$$<br><br>$$ = -{{3\Delta L} \over L} \times B$$<br><br>$$ \therefore $$ $$|{{\Delta L} \over L}| = {{\Delta P} \over {3B}}$$
<br><br>$$ \therefore $$ % change, $${{\Delta L} \over L} \t... | mcq | jee-main-2020-online-4th-september-evening-slot | 12,251 |
Ekt0hrzV4m2WY3xc7Kjgy2xukfrp9ah0 | physics | properties-of-matter | mechanical-properties-of-solids | An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its
frequency of oscillation along the vertical direction is : | [{"identifier": "A", "content": "$$f = {1 \\over {2\\pi }}\\sqrt {{{YA} \\over {mL}}} $$"}, {"identifier": "B", "content": "$$f = {1 \\over {2\\pi }}\\sqrt {{{mL} \\over {YA}}} $$"}, {"identifier": "C", "content": "$$f = {1 \\over {2\\pi }}\\sqrt {{{YL} \\over {mA}}} $$"}, {"identifier": "D", "content": "$$f = {1 \\ove... | ["A"] | null | An elastic wire can be treated as a spring with
<br><br>k = $${{YA} \over l}$$
<br><br>T = $$2\pi \sqrt {{m \over k}} $$
<br><br>$$ \Rightarrow $$ f = $${1 \over {2\pi }}\sqrt {{k \over m}} $$ = $${1 \over {2\pi }}\sqrt {{{YA} \over {ml}}} $$ | mcq | jee-main-2020-online-6th-september-morning-slot | 12,252 |
YXotwE6VkXcHCifO5o1klrhu9ll | physics | properties-of-matter | mechanical-properties-of-solids | If Y, K and $$\eta $$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters. | [{"identifier": "A", "content": "$$Y = {{9K\\eta } \\over {3K - \\eta }}N/{m^2}$$"}, {"identifier": "B", "content": "$$Y = {{9K\\eta } \\over {2\\eta + 3K}}N/{m^2}$$"}, {"identifier": "C", "content": "$$\\eta = {{3YK} \\over {9K + Y}}N/{m^2}$$"}, {"identifier": "D", "content": "$$K = {{Y\\eta } \\over {9\\eta - 3Y}}... | ["D"] | null | We know that,<br/><br/>$$Y = 3K(1 - 2\sigma )$$<br/><br/>$$ \Rightarrow \sigma = {1 \over 2}\left( {1 - {Y \over {3K}}} \right)$$ ..... (i)<br/><br/>Also, $$Y = 2\eta (1 + \sigma )$$<br/><br/>$$ \Rightarrow \sigma = {Y \over {2\eta }} - 1$$ .... (ii)<br/><br/>On comparing Eqs. (i) and (ii), we get<br/><br/>$$\left( {... | mcq | jee-main-2021-online-24th-february-morning-slot | 12,253 |
HwhTNbyVdytUQj4HJR1klropy90 | physics | properties-of-matter | mechanical-properties-of-solids | A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm. | [] | null | 2 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266124/exam_images/sugx7hnnueihl2gsu2ep.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 24th February Evening Shift Physics - Properties of Matter Question 165 English Explanation"><br><... | integer | jee-main-2021-online-24th-february-evening-slot | 12,254 |
HJBUayuAzuAhaoYvJH1kltjallu | physics | properties-of-matter | mechanical-properties-of-solids | The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be : | [{"identifier": "A", "content": "$${{\\rho K} \\over P}$$"}, {"identifier": "B", "content": "$${{PK} \\over \\rho }$$"}, {"identifier": "C", "content": "$${{\\rho P} \\over K}$$"}, {"identifier": "D", "content": "$${K \\over {\\rho P}}$$"}] | ["C"] | null | Bulk modulus $$K = {{ - \Delta P} \over {{{\Delta v} \over v}}} = {{ - \Delta Pv} \over {\Delta v}}$$<br><br>We know, $$\rho = {M \over V}$$<br><br>So, $${{ - \Delta \rho } \over \rho } = {{\Delta v} \over v}$$<br><br>$$K = {{ - \Delta P} \over {\left( { - {{\Delta \rho } \over \rho }} \right)}} = {{\rho \Delta P} \ov... | mcq | jee-main-2021-online-26th-february-morning-slot | 12,255 |
tNRj6vkhfycBqnaLWg1klulog2u | physics | properties-of-matter | mechanical-properties-of-solids | The length of metallic wire is l<sub>1</sub> when tension in it is T<sub>1</sub>. It is l<sub>2</sub> when the tension is T<sub>2</sub>. The original length of the wire will be : | [{"identifier": "A", "content": "$${{{T_1}{l_1} - {T_2}{l_2}} \\over {{T_2} - {T_1}}}$$"}, {"identifier": "B", "content": "$${{{l_1} + {l_2}} \\over 2}$$"}, {"identifier": "C", "content": "$${{{T_2}{l_1} + {T_1}{l_2}} \\over {{T_1} + {T_2}}}$$"}, {"identifier": "D", "content": "$${{{T_2}{l_1} - {T_1}{l_2}} \\over {{T_2... | ["D"] | null | Assuming Hooke's law to be valid.<br><br>$$T \propto (\Delta l)$$<br><br>$$T = k(\Delta l)$$<br><br>Let, l<sub>0</sub> = natural length (original length)<br><br>$$ \Rightarrow T = k(l - {l_0})$$<br><br>so, $${T_1} = k({l_1} - {l_0})$$ & $${T_2} = k({l_2} - {l_0})$$<br><br>$$ \Rightarrow {{{T_1}} \over {{T_2}}} = {{... | mcq | jee-main-2021-online-26th-february-evening-slot | 12,256 |
hYQiBj1dPUS2WLvS9b1kmkrry9q | physics | properties-of-matter | mechanical-properties-of-solids | Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expresse... | [] | null | 32 | $${\rho _A} = {\rho _B}$$<br><br>$${r _B} = 4{r _A}$$<br><br>$$\Delta {l_a} = 2$$ mm<br><br>$$\Delta {l_B} = 4$$ mm<br><br>$$y = {{stress} \over {strain}} = {{F/A} \over {\Delta l/l}}$$<br><br>$$ \Rightarrow $$ y$${{\Delta l} \over l} = {F \over {A}}$$<br><br>$$ \Rightarrow $$ $$l = {{Ay\Delta l} \over F}$$<br><br>$$ \... | integer | jee-main-2021-online-18th-march-morning-shift | 12,257 |
1krpoemx3 | physics | properties-of-matter | mechanical-properties-of-solids | The value of tension in a long thin metal wire has been changed from T<sub>1</sub> to T<sub>2</sub>. The lengths of the metal wire at two different values of tension T<sub>1</sub> and T<sub>2</sub> are l<sub>1</sub> and l<sub>2</sub> respectively. The actual length of the metal wire is : | [{"identifier": "A", "content": "$${{{l_1} + {l_2}} \\over 2}$$"}, {"identifier": "B", "content": "$$\\sqrt {{T_1}{T_2}{l_1}{l_2}} $$"}, {"identifier": "C", "content": "$${{{T_1}{l_2} - {T_2}{l_1}} \\over {{T_1} - {T_2}}}$$"}, {"identifier": "D", "content": "$${{{T_1}{l_1} - {T_2}{l_2}} \\over {{T_1} - {T_2}}}$$"}] | ["C"] | null | Suppose, I<sub>0</sub> be the actual length of metal wire and Y be its Young's modulus.<br/><br/>From Hooke's law,<br/><br/>$$Y = {{T{I_0}} \over {A\Delta I}}$$<br/><br/>where, $$\Delta I = I - {I_0}$$<br/><br/>$$ \Rightarrow Y = {{T{I_0}} \over {A(I - {I_0})}}$$ or $$I - I = {{T{I_0}} \over {AY}}$$<br/><br/>$$\therefo... | mcq | jee-main-2021-online-20th-july-morning-shift | 12,258 |
1krqb43b2 | physics | properties-of-matter | mechanical-properties-of-solids | The length of a metal wire is l<sub>1</sub>, when the tension in it is T<sub>1</sub> and is l<sub>2</sub> when the tension is T<sub>2</sub>. The natural length of the wire is : | [{"identifier": "A", "content": "$$\\sqrt {{l_1}{l_2}} $$"}, {"identifier": "B", "content": "$${{{l_1}{T_2} - {l_2}{T_1}} \\over {{T_2} - {T_1}}}$$"}, {"identifier": "C", "content": "$${{{l_1}{T_2} + {l_2}{T_1}} \\over {{T_2} + {T_1}}}$$"}, {"identifier": "D", "content": "$${{{l_1} + {l_2}} \\over 2}$$"}] | ["B"] | null | $${T_1} = k({l_1} - {l_0})$$<br><br>$${T_2} = k({l_2} - {l_0})$$<br><br>$${{{T_1}} \over {{T_2}}} = {{{l_1} - {l_0}} \over {{l_2} - {l_0}}}$$<br><br>$${{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}} = {l_0}$$ | mcq | jee-main-2021-online-20th-july-evening-shift | 12,259 |
1krukd8y4 | physics | properties-of-matter | mechanical-properties-of-solids | Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y<sub>1</sub> and Y<sub>2</sub>. The combination behaves as a single wire then its Young's modulus is : | [{"identifier": "A", "content": "$$Y = {{2{Y_1}{Y_2}} \\over {3({Y_1} + {Y_2})}}$$"}, {"identifier": "B", "content": "$$Y = {{2{Y_1}{Y_2}} \\over {{Y_1} + {Y_2}}}$$"}, {"identifier": "C", "content": "$$Y = {{{Y_1}{Y_2}} \\over {2({Y_1} + {Y_2})}}$$"}, {"identifier": "D", "content": "$$Y = {{{Y_1}{Y_2}} \\over {{Y_1} + ... | ["B"] | null | In series combination $$\Delta$$l = l<sub>1</sub> + l<sub>2</sub><br><br>$$Y = {{F/A} \over {\Delta l/l}} \Rightarrow \Delta l = {{Fl} \over {AY}}$$<br><br>$$ \Rightarrow \Delta l \propto {l \over Y}$$<br><br>Equivalent length of rod after joining is = 2l<br><br>As, lengths are same and force is also same in series<br>... | mcq | jee-main-2021-online-25th-july-morning-shift | 12,260 |
1ktbrqdrv | physics | properties-of-matter | mechanical-properties-of-solids | Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $${{24} \over \pi } \times {10^2}$$ Nm<sup>-2</sup>. What is the minimum radius of the wire ? (Take g = 10 ms<sup>-2</sup>)<br/><br/><img src="data:image/png;base64,UklGRlQNAABXRUJQVlA4IEgNAA... | [{"identifier": "A", "content": "125 cm"}, {"identifier": "B", "content": "1250 cm"}, {"identifier": "C", "content": "12.5 cm"}, {"identifier": "D", "content": "1.25 cm"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265342/exam_images/lcmolszldfnmjuvlpfoc.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th August Evening Shift Physics - Properties of Matter Question 141 English Explanation"> <br><b... | mcq | jee-main-2021-online-26th-august-evening-shift | 12,261 |
1ktfo660l | physics | properties-of-matter | mechanical-properties-of-solids | Wires W<sub>1</sub> and W<sub>2</sub> are made of same material having the breaking stress of 1.25 $$\times$$ 10<sup>9</sup> N/m<sup>2</sup>. W<sub>1</sub> and W<sub>2</sub> have cross-sectional area of 8 $$\times$$ 10<sup>$$-$$7</sup> m<sup>2</sup> and 4 $$\times$$ 10<sup>$$-$$7</sup> m<sup>2</sup>, respectively. Mass... | [] | null | 40 | B.S<sub>1</sub> = $${{{T_{1\max }}} \over {8 \times {{10}^{ - 7}}}}$$ $$\Rightarrow$$ T<sub>1 max</sub> = 8 $$\times$$ 1.25 $$\times$$ 100 = 1000 N<br><br>B.S<sub>2</sub> = $${{{T_{2\max }}} \over {4 \times {{10}^{ - 7}}}}$$ $$\Rightarrow$$ T<sub>2 max</sub> = 4 $$\times$$ 1.25 $$\times$$ 100 = 500 N<br><br>m = $${{500... | integer | jee-main-2021-online-27th-august-evening-shift | 12,262 |
1kth5n4f0 | physics | properties-of-matter | mechanical-properties-of-solids | When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. <br/><br/>(The bulk modulus of rubber = 9.8 $$\times$$ 10<sup>8</sup> Nm<sup>$$-$$2</sup>, Density of sea water = 10<sup>3</sup> kgm<sup>$$-$$3</sup>, g = 9.8 m/s<sup>2</sup>) | [] | null | 500 | $$B = - {{\Delta P} \over {\left( {{{\Delta V} \over V}} \right)}} = - {{\rho gh} \over {\left( {{{\Delta V} \over V}} \right)}}$$<br><br>$$ - {{B{{\Delta V} \over V}} \over {\rho g}} = h$$<br><br>$${{9.8 \times {{10}^8} \times 0.5} \over {100 \times {{10}^3} \times 9.8}} = h$$<br><br>h = 500 | integer | jee-main-2021-online-31st-august-morning-shift | 12,264 |
1ktjmub5w | physics | properties-of-matter | mechanical-properties-of-solids | Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 10<sup>3</sup> kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 10<sup>11</su... | [{"identifier": "A", "content": "3.60 $$\\times$$ 10<sup>$$-$$8</sup>"}, {"identifier": "B", "content": "2.60 $$\\times$$ 10<sup>$$-$$7</sup>"}, {"identifier": "C", "content": "1.87 $$\\times$$ 10<sup>$$-$$3</sup>"}, {"identifier": "D", "content": "7.07 $$\\times$$ 10<sup>$$-$$4</sup>"}] | ["B"] | null | Force on each column = $${{mg} \over 4}$$<br><br>Strain = $${{mg} \over {4AY}}$$<br><br>$$ = {{50 \times {{10}^3} \times 9.8} \over {4 \times \pi (1 - 0.25) \times 2 \times {{10}^{11}}}}$$<br><br>= 2.6 $$\times$$ 10<sup>$$-$$7</sup> | mcq | jee-main-2021-online-31st-august-evening-shift | 12,265 |
1l5471gh6 | physics | properties-of-matter | mechanical-properties-of-solids | <p>A wire of length L is hanging from a fixed support. The length changes to L<sub>1</sub> and L<sub>2</sub> when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :</p> | [{"identifier": "A", "content": "$$\\sqrt {{L_1}{L_2}} $$"}, {"identifier": "B", "content": "$${{{L_1} + {L_2}} \\over 2}$$"}, {"identifier": "C", "content": "$$2{L_1} - {L_2}$$"}, {"identifier": "D", "content": "$$3{L_1} - 2{L_2}$$"}] | ["C"] | null | <p>$$y = {{FL} \over {A\Delta L}}$$</p>
<p>$$ \Rightarrow \Delta L = {{FL} \over {Ay}}$$</p>
<p>$$ \Rightarrow {L_1} = L + {{(1g)L} \over {Ay}}$$ ..... (i)</p>
<p>and $${L_2} = L + {{(2g)L} \over {Ay}}$$ ..... (ii)</p>
<p>$$ \Rightarrow L = 2{L_1} - {L_2}$$</p> | mcq | jee-main-2022-online-29th-june-morning-shift | 12,266 |
1l58czda7 | physics | properties-of-matter | mechanical-properties-of-solids | <p>The elongation of a wire on the surface of the earth is 10<sup>$$-$$4</sup> m. The same wire of same dimensions is elongated by 6 $$\times$$ 10<sup>$$-$$5</sup> m on another planet. The acceleration due to gravity on the planet will be ____________ ms<sup>$$-$$2</sup>. (Take acceleration due to gravity on the surfac... | [] | null | 6 | <p>on earth, $$\Delta l = {10^{ - 4}}\,m$$</p>
<p>on other planet $$\Delta l' = 6 \times {10^{ - 5}}\,m$$</p>
<p>$$\Delta l = {{Fl} \over {Ay}} \Rightarrow {{\Delta l'} \over {\Delta l}} = {{{{F'l} \over {Ay}}} \over {{{Fl} \over {Ay}}}} = {{mg'} \over {mg}}$$</p>
<p>$$ \Rightarrow g' = {{\Delta l'} \over {\Delta l}} \... | integer | jee-main-2022-online-26th-june-morning-shift | 12,267 |
1l5bbwgkf | physics | properties-of-matter | mechanical-properties-of-solids | <p>Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :</p> | [{"identifier": "A", "content": "$${\\left( {{A \\over B}} \\right)^{{1 \\over 5}}}$$"}, {"identifier": "B", "content": "$${\\left( {{B \\over A}} \\right)^{{1 \\over 5}}}$$"}, {"identifier": "C", "content": "$${\\left( {{2A \\over B}} \\right)^{{1 \\over 5}}}$$"}, {"identifier": "D", "content": "$${\\left( {{B \\over ... | ["C"] | null | <p>For equilibrium</p>
<p>$$ - {{dU} \over {dr}} = 0 = {{10A} \over {{r^{11}}}} - {{5B} \over {{r^6}}}$$</p>
<p>$$ \Rightarrow {r^5} = {{2A} \over B}$$</p>
<p>And $$r = {\left( {{{2A} \over B}} \right)^{1/5}}$$</p> | mcq | jee-main-2022-online-24th-june-evening-shift | 12,268 |
1l5c2lxov | physics | properties-of-matter | mechanical-properties-of-solids | <p>The bulk modulus of a liquid is 3 $$\times$$ 10<sup>10</sup> Nm<sup>$$-$$2</sup>. The pressure required to reduce the volume of liquid by 2% is :</p> | [{"identifier": "A", "content": "3 $$\\times$$ 10<sup>8</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "B", "content": "9 $$\\times$$ 10<sup>8</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "C", "content": "6 $$\\times$$ 10<sup>8</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "D", "content": "12 $$\\times$$ 10<sup>8</sup> Nm<su... | ["C"] | null | <p>$$\because$$ $$B = {{\Delta P} \over {\left( { - {{\Delta V} \over V}} \right)}}$$</p>
<p>$$ \Rightarrow \Delta P = 3 \times {10^{10}} \times (0.02)$$</p>
<p>$$ = 6 \times {10^8}$$ N/m<sup>2</sup></p> | mcq | jee-main-2022-online-24th-june-morning-shift | 12,269 |
1l6gnmpdg | physics | properties-of-matter | mechanical-properties-of-solids | <p>In an experiment to determine the Young's modulus of wire of a length exactly $$1 \mathrm{~m}$$, the extension in the length of the wire is measured as $$0.4 \mathrm{~mm}$$ with an uncertainty of $$\pm\, 0.02 \mathrm{~mm}$$ when a load of $$1 \mathrm{~kg}$$ is applied. The diameter of the wire is measured as $$0.4 \... | [] | null | 2 | <p>$${{F/A} \over {l/L}} = Y,\,A = \pi {D^2}$$</p>
<p>$${{\Delta Y} \over Y} = {{\Delta F} \over F} + {{2\Delta D} \over D} + {{\Delta l} \over e} + {{\Delta L} \over L}$$</p>
<p>$$ = 2 \times {{0.01} \over {0.4}} + {{0.02} \over {0.4}}$$</p>
<p>$$ = {{0.04} \over {0.4}} = {1 \over {10}}$$</p>
<p>$$Y = {{Fl} \over {A\D... | integer | jee-main-2022-online-26th-july-morning-shift | 12,271 |
1l6i1u0sy | physics | properties-of-matter | mechanical-properties-of-solids | <p>The area of cross section of the rope used to lift a load by a crane is $$2.5 \times 10^{-4} \mathrm{~m}^{2}$$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be :</p>
<p>(take $$g=10 ... | [{"identifier": "A", "content": "$$6.25\\times 10^{-4} \\mathrm{~m}^{2}$$"}, {"identifier": "B", "content": "$$10\\times 10^{-4} \\mathrm{~m}^{2}$$"}, {"identifier": "C", "content": "$$1\\times 10^{-4} \\mathrm{~m}^{2}$$"}, {"identifier": "D", "content": "$$1.67\\times 10^{-4} \\mathrm{~m}^{2}$$"}] | ["A"] | null | <p>The relationship between stress (σ), force (F), and area (A) is given by :</p>
<p>$$\sigma = \frac{F}{A}$$</p>
<p>In this context, the force is equal to the weight of the load, so we can substitute force with mass (m) times gravity (g) :</p>
<p>$$F = m \cdot g$$</p>
<p>From this, we get the formula for the cross-sec... | mcq | jee-main-2022-online-26th-july-evening-shift | 12,272 |
1l6i3mlyw | physics | properties-of-matter | mechanical-properties-of-solids | <p>A uniform heavy rod of mass $$20 \mathrm{~kg}$$, cross sectional area $$0.4 \mathrm{~m}^{2}$$ and length $$20 \mathrm{~m}$$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $$x \times 10^{-9} \mathrm{~m}$$. The value of $$x$$ is _______________.<... | [] | null | 25 | <p>$${{{F \over A}} \over {{{\Delta L} \over L}}} = Y$$</p>
<p>$$\Delta L = {{FL} \over {AY}} = {{{T_{avg}}L} \over {AY}} = {{MgL} \over {2AY}}$$</p>
<p>$$ = {{20 \times 10 \times 20} \over {2 \times 0.4 \times 2 \times {{10}^{11}}}} = {{4 \times {{10}^3} \times {{10}^{ - 11}}} \over {4 \times 0.4}}$$</p>
<p>$$ = 2.5 \... | integer | jee-main-2022-online-26th-july-evening-shift | 12,273 |
1l6ntp3ah | physics | properties-of-matter | mechanical-properties-of-solids | <p>A string of area of cross-section $$4 \mathrm{~mm}^{2}$$ and length $$0.5 \mathrm{~m}$$ is connected with a rigid body of mass $$2 \mathrm{~kg}$$. The body is rotated in a vertical circular path of radius $$0.5 \mathrm{~m}$$. The body acquires a speed of $$5 \mathrm{~m} / \mathrm{s}$$ at the bottom of the circular p... | [] | null | 30 | <p>$$A = 4 \times {10^{ - 6}}$$ m<sup>2</sup></p>
<p>$$l = 0.5$$ m</p>
<p>$$m = 2$$ kg</p>
<p>$${v_b} = 5$$ m/s</p>
<p>$${T_b} = mg + m\left( {{{V_b^2} \over l}} \right)$$</p>
<p>$$ = 20 + 2 \times {{25} \over {{1 \over 2}}} = 120$$ N</p>
<p>$${{\Delta l} \over l} = {{{T_b}} \over A} \times {1 \over Y} = {{120} \over {... | integer | jee-main-2022-online-28th-july-evening-shift | 12,277 |
1l6p4eiz0 | physics | properties-of-matter | mechanical-properties-of-solids | <p>If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :</p> | [{"identifier": "A", "content": "remain same"}, {"identifier": "B", "content": "become 8 times its initial value"}, {"identifier": "C", "content": "become $$\\frac{1}{4}$$ of its initial value"}, {"identifier": "D", "content": "become 4 times its initial value"}] | ["A"] | null | <p>Young's modulus of matter depends on material of wire and is independent of the dimensions of the wire. As the material remains same so Young's modulus also remain same.</p> | mcq | jee-main-2022-online-29th-july-morning-shift | 12,278 |
1l6rik7mm | physics | properties-of-matter | mechanical-properties-of-solids | <p>A metal wire of length $$0.5 \mathrm{~m}$$ and cross-sectional area $$10^{-4} \mathrm{~m}^{2}$$ has breaking stress $$5 \times 10^{8} \,\mathrm{Nm}^{-2}$$. A block of $$10 \mathrm{~kg}$$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be ________... | [] | null | 50 | $\mathrm{T}=\frac{\mathrm{mv}^2}{\ell}=\frac{10 \times \mathrm{v}^2}{0.5}=20 \mathrm{v}^2$
<br/><br/>$\mathrm{~T}_{\max }=$ Breaking stress $\times$ Area
<br/><br/>$=5 \times 10^8 \times 10^{-4}=5 \times 10^4$
<br/><br/>$20 \mathrm{~V}^2=5 \times 10^4$
<br/><br/>$\mathrm{~V}=\sqrt{\frac{1}{4} \times 10^4}=50 \mathrm{~m... | integer | jee-main-2022-online-29th-july-evening-shift | 12,279 |
1l6riu824 | physics | properties-of-matter | mechanical-properties-of-solids | <p>The speed of a transverse wave passing through a string of length $$50 \mathrm{~cm}$$ and mass $$10 \mathrm{~g}$$ is $$60 \mathrm{~ms}^{-1}$$. The area of cross-section of the wire is $$2.0 \mathrm{~mm}^{2}$$ and its Young's modulus is $$1.2 \times 10^{11} \mathrm{Nm}^{-2}$$. The extension of the wire over its natur... | [] | null | 15 | $\mathrm{V}_{\mathrm{w}}=\sqrt{\frac{\mathrm{T}}{\mu}}$
<br/><br/>$60=\sqrt{\frac{\mathrm{T}}{10 \times 10^{-3}} \times 0.5}$
<br/><br/>$\mathrm{~T}=\frac{(60)^2 \times 10^{-2}}{0.5}=72 \mathrm{~N}$
<br/><br/>$\Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{AY}}=\frac{72 \times 0.5}{2 \times 10^{-6} \times 1.2 \times 10^{11... | integer | jee-main-2022-online-29th-july-evening-shift | 12,280 |
1ldnwwl5p | physics | properties-of-matter | mechanical-properties-of-solids | <p>The Young's modulus of a steel wire of length $$6 \mathrm{~m}$$ and cross-sectional area $$3 \mathrm{~mm}^{2}$$, is $$2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}$$. The wire is suspended from its support on a given planet. A block of mass $$4 \mathrm{~kg}$$ is attached to the free end of the wire. The acceleration ... | [{"identifier": "A", "content": "0.1 cm"}, {"identifier": "B", "content": "1 cm"}, {"identifier": "C", "content": "0.1 mm"}, {"identifier": "D", "content": "1 mm"}] | ["C"] | null | The elongation of the wire can be calculated using the formula for stress and strain. The stress in the wire is given by:
<br/><br/>$$\sigma = \frac{mg}{A}$$
<br/><br/>where m is the mass of the block (4 kg), g is the acceleration due to gravity on the planet (1/4 of its value on the earth, or 2.5 m/s<sup>2</sup>), a... | mcq | jee-main-2023-online-1st-february-evening-shift | 12,281 |
ldquvoem | physics | properties-of-matter | mechanical-properties-of-solids | A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2 \mathrm{~mm}$. If same force is applied to another steel wire ' $\mathrm{B}$ ' of double the length and a diameter $2.4$ times that of the wire ' $\mathrm{A}$ ', the elongation in the wire ' $\mathrm{B}$ ' wil... | [{"identifier": "A", "content": "$6 .9 \\times 10^{-2} \\mathrm{~mm}$"}, {"identifier": "B", "content": "$6.06 \\times 10^{-2} \\mathrm{~mm}$"}, {"identifier": "C", "content": "$2.77 \\times 10^{-2} \\mathrm{~mm}$"}, {"identifier": "D", "content": "$3.0 \\times 10^{-2} \\mathrm{~mm}$"}] | ["A"] | null | <p>$$\because$$ $$\Delta l = {{Fl(4)} \over {Y\pi {d^2}}}$$</p>
<p>$${{\Delta {l_1}} \over {\Delta {l_2}}} = {{\Delta {l_1}} \over {d_1^2}} \times {{d_2^2} \over {{l_2}}}$$</p>
<p>$${{0.2} \over {\Delta {l_2}}} = {1 \over 2} \times {(2.4)^2}$$</p>
<p>$$\Delta {l_2} = {{2 \times 0.2} \over {{{(2.4)}^2}}}$$</p>
<p>$$ = 6... | mcq | jee-main-2023-online-30th-january-evening-shift | 12,285 |
1ldwrer3c | physics | properties-of-matter | mechanical-properties-of-solids | <p>Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R</p>
<p>Assertion A : Steel is used in the construction of buildings and bridges.</p>
<p>Reason R : Steel is more elastic and its elastic limit is high.</p>
<p>In the light of above statements, choose the most appropr... | [{"identifier": "A", "content": "Both A and R are correct and R is the correct explanation of A"}, {"identifier": "B", "content": "A is correct but R is not correct"}, {"identifier": "C", "content": "Both A and R are correct but R is NOT the correct explanation of A"}, {"identifier": "D", "content": "A is not correct b... | ["A"] | null | <p><b>Assertion A</b> states that steel is used in the construction of buildings and bridges, which is true. Steel is a widely used material for construction due to its high strength, durability, and resistance to corrosion.
</p>
<p><b>Reason R</b> states that steel is more elastic and has a higher elastic limit compar... | mcq | jee-main-2023-online-24th-january-evening-shift | 12,287 |
1ldyd0l6c | physics | properties-of-matter | mechanical-properties-of-solids | <p>A 100 m long wire having cross-sectional area $$\mathrm{6.25\times10^{-4}~m^2}$$ and Young's modulus is $$\mathrm{10^{10}~Nm^{-2}}$$ is subjected to a load of 250 N, then the elongation in the wire will be :</p> | [{"identifier": "A", "content": "$$\\mathrm{6.25\\times10^{-6}~m}$$"}, {"identifier": "B", "content": "$$\\mathrm{4\\times10^{-3}~m}$$"}, {"identifier": "C", "content": "$$\\mathrm{4\\times10^{-4}~m}$$"}, {"identifier": "D", "content": "$$\\mathrm{6.25\\times10^{-3}~m}$$"}] | ["B"] | null | Elongation in wire $\delta=\frac{\mathrm{F} \ell}{\mathrm{AY}}$<br/><br/>
$$
\begin{aligned}
& \delta=\frac{250 \times 100}{6.25 \times 10^{-4} \times 10^{10}} \\\\
& \delta=4 \times 10^{-3} \mathrm{~m}
\end{aligned}
$$ | mcq | jee-main-2023-online-24th-january-morning-shift | 12,288 |
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