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lgnx23k6 | physics | properties-of-matter | mechanical-properties-of-solids | A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by ' $l$ '. Another wire of same material of length ' $2 \mathrm{~L}$ ' and radius ' $2 r$ ' is pulled by a force ' $2 f$ '. Then the increase in its length will be : | [{"identifier": "A", "content": "$2 l$"}, {"identifier": "B", "content": "$4 l$"}, {"identifier": "C", "content": "$l$"}, {"identifier": "D", "content": "$l / 2$"}] | ["C"] | null | Let $A$ be the cross-sectional area of the first wire, and let $Y$ be its Young's modulus.<br/><br/> The strain in the wire is given by $\epsilon = \frac{l}{L}$, where $l$ is the increase in length. The stress in the wire is given by $\sigma = \frac{f}{A}$. <br/><br/>According to Hooke's law, the stress is proportional... | mcq | jee-main-2023-online-15th-april-morning-shift | 12,289 |
1lgq2fq2p | physics | properties-of-matter | mechanical-properties-of-solids | <p>Under isothermal condition, the pressure of a gas is given by $$\mathrm{P}=a \mathrm{~V}^{-3}$$, where $$a$$ is a constant and $$\mathrm{V}$$ is the volume of the gas. The bulk modulus at constant temperature is equal to</p> | [{"identifier": "A", "content": "$$\\frac{P}{2}$$"}, {"identifier": "B", "content": "2 P"}, {"identifier": "C", "content": "3 P"}, {"identifier": "D", "content": "P"}] | ["C"] | null | The bulk modulus ($$B$$) of a substance is defined as the ratio of the infinitesimal pressure increase ($$\Delta P$$) to the relative decrease in volume ($$\frac{-\Delta V}{V}$$) at constant temperature:
<br/><br/>
$$B = -V \frac{\Delta P}{\Delta V}$$
<br/><br/>
To find the bulk modulus for the given pressure-volume re... | mcq | jee-main-2023-online-13th-april-morning-shift | 12,290 |
1lguyq0b4 | physics | properties-of-matter | mechanical-properties-of-solids | <p>The length of a wire becomes $$l_{1}$$ and $$l_{2}$$ when $$100 \mathrm{~N}$$ and $$120 \mathrm{~N}$$ tensions are applied respectively. If $$10 ~l_{2}=11~ l_{1}$$, the natural length of wire will be $$\frac{1}{x} ~l_{1}$$. Here the value of $$x$$ is _____________.</p> | [] | null | 2 | <p>Given:</p>
<ol>
<li>When tension $$T_1 = 100 \mathrm{~N}$$, extension $$= l_1 - l_0$$.</li>
<li>When tension $$T_2 = 120 \mathrm{~N}$$, extension $$= l_2 - l_0$$.</li>
</ol>
<p>Now, let's write the equations using Hooke's Law:</p>
<p>$$100 = k(l_1 - l_0)$$</p>
<p>$$120 = k(l_2 - l_0)$$</p>
<p>Divide the firs... | integer | jee-main-2023-online-11th-april-morning-shift | 12,292 |
1lgvruaf1 | physics | properties-of-matter | mechanical-properties-of-solids | <p>Young's moduli of the material of wires A and B are in the ratio of $$1: 4$$, while its area of cross sections are in the ratio of $$1: 3$$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ will be in the ratio of</p>
<p>[Assume... | [{"identifier": "A", "content": "1 : 12"}, {"identifier": "B", "content": "1 : 36"}, {"identifier": "C", "content": "12 : 1"}, {"identifier": "D", "content": "36 : 1"}] | ["C"] | null | <p>Given the formula for elongation in a material due to a force:</p>
<p>$$
\Delta L = \frac{FL}{AY}
$$</p>
<p>where:</p>
<ul>
<li>F is the force applied,</li>
<li>L is the original length,</li>
<li>A is the cross-sectional area of the material, and</li>
<li>Y is Young's modulus of the material.</li>
</ul>
<p>The r... | mcq | jee-main-2023-online-10th-april-evening-shift | 12,293 |
1lgyfxgqw | physics | properties-of-matter | mechanical-properties-of-solids | <p>Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $$\times$$ 10$$^{-6}$$ m. [Young's modulus for steel = 2 $$\times$$ 10$$^{11}$$ Nm$$^{-2}$$ and g = 10 ms$$^{-2}$$ ]</p>
<p><img src="da... | [] | null | 20 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1loefepjb/e45d1b02-d43d-4ca7-93ff-bc1ebf822797/0a228d70-77fa-11ee-813b-df032ba76c91/file-6y3zli1loefepjc.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1loefepjb/e45d1b02-d43d-4ca7-93ff-bc1ebf822797/0a228d70-77fa-11ee-81... | integer | jee-main-2023-online-10th-april-morning-shift | 12,294 |
1lh028g0a | physics | properties-of-matter | mechanical-properties-of-solids | <p>An aluminium rod with Young's modulus $$Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$ undergoes elastic strain of $$0.04 \%$$. The energy per unit volume stored in the rod in SI unit is:</p> | [{"identifier": "A", "content": "5600"}, {"identifier": "B", "content": "2800"}, {"identifier": "C", "content": "11200"}, {"identifier": "D", "content": "8400"}] | ["A"] | null | <p>The strain energy stored per unit volume in a material under stress can be calculated using the following formula:</p>
<p>$U = \frac{1}{2} \sigma \epsilon$</p>
<p>where $\sigma$ is the stress and $\epsilon$ is the strain. </p>
<p>For an elastic material, stress is proportional to strain (Hooke's law), and the co... | mcq | jee-main-2023-online-8th-april-morning-shift | 12,295 |
1lh25wfvf | physics | properties-of-matter | mechanical-properties-of-solids | <p>A steel rod has a radius of $$20 \mathrm{~mm}$$ and a length of $$2.0 \mathrm{~m}$$. A force of $$62.8 ~\mathrm{kN}$$ stretches it along its length. Young's modulus of steel is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$. The longitudinal strain produced in the wire is _____________ $$\times 10^{-5}$$</p> | [] | null | 25 | $$
\begin{aligned}
& \text { Strain }=\frac{\text { stress }}{Y}=\frac{\frac{62.8 \times 10^3}{\pi \times(0.02)^2}}{2 \times 10^{11}} \\\\
& =\frac{62.8 \times 10^3}{3.14 \times 4 \times 10^{-4} \times 2 \times 10^{11}} \\\\
& =2.5 \times 10^{-4} \\\\
& =25 \times 10^{-5}
\end{aligned}
$$ | integer | jee-main-2023-online-6th-april-morning-shift | 12,296 |
1lh31om75 | physics | properties-of-matter | mechanical-properties-of-solids | <p>A metal block of mass $$\mathrm{m}$$ is suspended from a rigid support through a metal wire of diameter $$14 \mathrm{~mm}$$. The tensile stress developed in the wire under equilibrium state is $$7 \times 10^{5} \mathrm{Nm}^{-2}$$. The value of mass $$\mathrm{m}$$ is _________ $$\mathrm{kg}$$. (Take, $$\mathrm{g}=9.8... | [] | null | 11 | <p>To find the mass $$m$$ of the metal block, we need to consider the tensile stress developed in the wire. The formula for tensile stress is:</p>
<p>$$\text{Tensile Stress} = \frac{\text{Force}}{\text{Area}}$$</p>
<p>The force acting on the wire is the weight of the metal block, which can be represented as $$F = mg$$.... | integer | jee-main-2023-online-6th-april-evening-shift | 12,297 |
lsanfj48 | physics | properties-of-matter | mechanical-properties-of-solids | One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.<br/... | [] | null | 3 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsc0far1/4bfa6ca4-4e8a-41c5-8282-35ff047c473e/bdcd5dd0-c5d6-11ee-baf2-61ef5327b65c/file-6y3zli1lsc0far2.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsc0far1/4bfa6ca4-4e8a-41c5-8282-35ff047c473e/bdcd5dd0-c5d6-11ee-ba... | integer | jee-main-2024-online-1st-february-evening-shift | 12,298 |
jaoe38c1lsd8b0eu | physics | properties-of-matter | mechanical-properties-of-solids | <p>Two blocks of mass $$2 \mathrm{~kg}$$ and $$4 \mathrm{~kg}$$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $$4.0 \times 10^{-5} \mathrm{~m}$$ and Young's modulus of the metal is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$$. The longitudinal strain developed i... | [] | null | 12 | <p>$$\begin{aligned}
& \mathrm{T}=\left(\frac{2 \mathrm{~m}_1 \mathrm{~m}_2}{\mathrm{~m}_1+\mathrm{m}_2}\right) \mathrm{g}=\frac{80}{3} \mathrm{~N} \\
& \mathrm{~A}=\pi \mathrm{r}^2=16 \pi \times 10^{-10} \mathrm{~m}^2 \\
& \text { Strain }=\frac{\Delta \ell}{\ell}=\frac{\mathrm{F}}{\mathrm{AY}}=\frac{\mathrm{T}}{\math... | integer | jee-main-2024-online-31st-january-evening-shift | 12,301 |
jaoe38c1lsflradt | physics | properties-of-matter | mechanical-properties-of-solids | <p>A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length increases by $$l$$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:</p> | [{"identifier": "A", "content": "2 times"}, {"identifier": "B", "content": "4 times"}, {"identifier": "C", "content": "3 times"}, {"identifier": "D", "content": "$$\\frac{3}{2}$$ times"}] | ["A"] | null | <p>$$\begin{aligned}
& Y=\frac{\text { stress }}{\text { strain }} \\
& Y=\frac{\frac{\mathrm{F}}{\frac{\pi \mathrm{r}^2}{\ell}}}{\frac{\ell}{\mathrm{L}}}
\end{aligned}$$</p>
<p>$$\mathrm{F}=\mathrm{Y} \pi \mathrm{r}^2 \times \frac{\ell}{\mathrm{L}} \quad \text{.... (i)}$$</p>
<p>$$\begin{aligned}
& \mathrm{Y}=\frac{\f... | mcq | jee-main-2024-online-29th-january-evening-shift | 12,302 |
jaoe38c1lsfmbbbf | physics | properties-of-matter | mechanical-properties-of-solids | <p>Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections are in the ratio $$4: 1$$ and force $$F_1$$ is applied to $$P$$, an extension of $$\Delta l$$ is produced. The force which is required to produce same extension in $$Q$$ is $$\mathrm{F}_2$$.<br/><br/... | [] | null | 16 | <p>$$\mathrm{Y}=\frac{\text { Stress }}{\text { Strain }}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \ell / \ell}=\frac{\mathrm{F} \ell}{\mathrm{A} \Delta \ell}$$</p>
<p>$$\begin{aligned}
& \Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{AY}} \\
& \mathrm{V}=\mathrm{A} \ell \Rightarrow \ell=\frac{\mathrm{V}}{\mathrm{A}} \\
& \De... | integer | jee-main-2024-online-29th-january-evening-shift | 12,303 |
1lsgx5dwc | physics | properties-of-matter | mechanical-properties-of-solids | <p>Young's modules of material of a wire of length '$$L$$' and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :</p> | [{"identifier": "A", "content": "4 Y"}, {"identifier": "B", "content": "2 Y"}, {"identifier": "C", "content": "$$\\mathrm{\\frac{Y}{4}}$$"}, {"identifier": "D", "content": "Y"}] | ["D"] | null | <p>Young's modulus depends on the material not length and cross sectional area. So young's modulus remains same.</p> | mcq | jee-main-2024-online-30th-january-morning-shift | 12,304 |
1lsgxkprt | physics | properties-of-matter | mechanical-properties-of-solids | <p>Each of three blocks $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ shown in figure has a mass of $$3 \mathrm{~kg}$$. Each of the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ has cross-sectional area $$0.005 \mathrm{~cm}^2$$ and Young's modulus $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Neglecting friction, the lo... | [] | null | 2 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsqm5e63/72fafd17-bfb1-40a2-af0d-c7b9090f3edf/ac48ccb0-cdde-11ee-a0d3-7b75c4537559/file-6y3zli1lsqm5e64.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsqm5e63/72fafd17-bfb1-40a2-af0d-c7b9090f3edf/ac48ccb0-cdde-11ee... | integer | jee-main-2024-online-30th-january-morning-shift | 12,305 |
lv0vy0ap | physics | properties-of-matter | mechanical-properties-of-solids | <p>An elastic spring under tension of $$3 \mathrm{~N}$$ has a length $$a$$. Its length is $$b$$ under tension $$2 \mathrm{~N}$$. For its length $$(3 a-2 b)$$, the value of tension will be _______ N.</p> | [] | null | 5 | <p>To determine the tension for the elastic spring's length of $$(3a - 2b)$$, we can use Hooke's law which states that the force exerted by a spring is proportional to the extension or compression of the spring from its natural length. Mathematically, Hooke's law is given by:</p>
<p>
<p>$$ F = k \cdot \Delta x $$</p>... | integer | jee-main-2024-online-4th-april-morning-shift | 12,307 |
lv7v3obt | physics | properties-of-matter | mechanical-properties-of-solids | <p>The density and breaking stress of a wire are $$6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$$ and $$1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{\text {rd }}$$ of the value on the surface of earth. ... | [] | null | 600 | <p>The breaking stress of a wire, denoted as $$\sigma$$, is the maximum tension per unit area it can withstand before it breaks. It is given as:
<p>$ \sigma = \frac{F}{A} $</p>
<p>where $F$ is the breaking force and $A$ is the cross-sectional area of the wire. The weight of the wire, when it's on the verge of breakin... | integer | jee-main-2024-online-5th-april-morning-shift | 12,309 |
lvb2acm6 | physics | properties-of-matter | mechanical-properties-of-solids | <p>A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and length $$2 \mathrm{~m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \mathrm{~kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta=\frac{1}{100}$$ rad... | [] | null | 1 | <p>$$\begin{aligned}
\Delta I_{\text {spring }} & =\left(\sqrt{L^2+x^2}\right)-L \\
& =\frac{x^2}{2 L} \\
T=k \Delta I & =\frac{k n^2}{2 L}
\end{aligned}$$</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lwbjb8c8/38e9be6c-cd47-49ee-8647-258f37fcf2b4/af05e780-14c4-11ef-b239-251b0141b7... | integer | jee-main-2024-online-6th-april-evening-shift | 12,311 |
w7r7nIfnfp8jOQI2 | physics | properties-of-matter | newton's-law-of-cooling | According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left( {\Delta \theta } \right)^n},$$ where $${\Delta \theta }$$ is the difference of the temperature of the body and the surrounding, and $$n$$ is equal to : | [{"identifier": "A", "content": "two "}, {"identifier": "B", "content": "three "}, {"identifier": "C", "content": "four "}, {"identifier": "D", "content": "one "}] | ["D"] | null | <p>Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. Mathematically, this law is often written as :</p>
<p>$ \frac{d\theta}{dt} \propto \Delta \theta $</p>
<p>In this formula, $ \frac{d\theta}{dt} $ is the rat... | mcq | aieee-2003 | 12,312 |
QGJEaNzSsvCYE8r5 | physics | properties-of-matter | newton's-law-of-cooling | A liquid in a beaker has temperature $$\theta \left( t \right)$$ at time $$t$$ and $${\theta _0}$$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $${\log _e}\left( {\theta - {\theta _0}} \right)$$ and $$t$$ is : | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263393/exam_images/j6ap9ig8cq64upurlvlo.webp\" loading=\"lazy\" alt=\"AIEEE 2012 Physics - Properties of Matter Question 225 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"qu... | ["A"] | null | Newton's law of cooling
<br><br/>$${{d\theta } \over {dt}} = - k\left( {\theta - {\theta _0}} \right)$$
<br><br/>$$ \Rightarrow {{d\theta } \over {\left( {\theta - {\theta _0}} \right)}} = - kdt$$
<p>Intergrating
<br><br/>$$ \Rightarrow \log \left( {\theta - {\theta _0}} \right) = - kt + c$$
<br><br/>Which repres... | mcq | aieee-2012 | 12,313 |
KXQRaTE2ah8J9qF2 | physics | properties-of-matter | newton's-law-of-cooling | If a piece of metal is heated to temperature $$\theta $$ and then allowed to cool in a room which is at temperature $${\theta _0},$$ the graph between the temperature $$T$$ of the metal and time $$t$$ will be closest to | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266405/exam_images/m9qa7uewongovofec2mm.webp\" loading=\"lazy\" alt=\"JEE Main 2013 (Offline) Physics - Properties of Matter Question 224 English Option 1\"> "}, {"identifier": "B", "content": "<i... | ["C"] | null | According to Newton's law of cooling, the temperature goes on decreasing with time non-linearly. | mcq | jee-main-2013-offline | 12,314 |
upiqi3NbJ5zDvUnNC00u8 | physics | properties-of-matter | newton's-law-of-cooling | A body takes 10 minutes to cool from 60<sup>o</sup>C to 50<sup>o</sup>C. The tempertature of surroundings is constant at 25<sup>o</sup>C. Then, the temperature of the body after next 10 minutes will be approximately : | [{"identifier": "A", "content": "47<sup>o</sup>C"}, {"identifier": "B", "content": "41<sup>o</sup>C"}, {"identifier": "C", "content": "45<sup>o</sup>C"}, {"identifier": "D", "content": "43<sup>o</sup>C"}] | ["D"] | null | <p>Time taken to cool from 60$$^\circ$$C to 50$$^\circ$$C = 10 minutes</p>
<p>Temperature of surroundings = 25$$^\circ$$C</p>
<p>Temperature of body in next 10 minutes = T</p>
<p>Therefore, $${{60 - 50} \over {10\,\min }} = {k_B}\left[ {{{60 + 50} \over 2} - 25} \right] \Rightarrow {k_B}30 = 1$$ ...... (1)</p>
<p>and $... | mcq | jee-main-2018-online-15th-april-evening-slot | 12,315 |
1kryxujac | physics | properties-of-matter | newton's-law-of-cooling | A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the body to cool from 51$$^\circ$$ C to 49$$^\circ$$ C is : | [{"identifier": "A", "content": "4 min."}, {"identifier": "B", "content": "3 min."}, {"identifier": "C", "content": "8 min."}, {"identifier": "D", "content": "6 min."}] | ["D"] | null | $${{\Delta T} \over {\Delta t}} = K({T_t} - {T_s})$$<br><br>T<sub>t</sub> = average temp.<br><br><sub>T</sub> = surrounding temp.<br><br>$${{61 - 59} \over 4} = K\left( {{{61 + 59} \over 2} - 30} \right)$$ ..... (1)<br><br>$${{51 - 49} \over t} = K\left( {{{51 + 49} \over 2} - 30} \right)$$ ..... (2)<br><br>Divide (1) ... | mcq | jee-main-2021-online-27th-july-morning-shift | 12,318 |
1lduhzscr | physics | properties-of-matter | newton's-law-of-cooling | <p>A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will take to cool from 75$$^\circ$$C to 69$$^\circ$$C?</p> | [{"identifier": "A", "content": "2 minutes"}, {"identifier": "B", "content": "0.5 minute"}, {"identifier": "C", "content": "1.4 minutes"}, {"identifier": "D", "content": "1 minute"}] | ["C"] | null | From Newton's law of cooling.
<br/><br/>
$$
\frac{d T}{d t}=-k\left(T-T_{s}\right)
$$
<br/><br/>
Case $\mathrm{I}: d T=12^{\circ} \mathrm{C}, d t=2 \min$
<br/><br/>
$$
\frac{12}{2}=-k\left[92-22^{\circ}\right]=-k 70
$$
<br/><br/>
Case II : $d T=6^{\circ} \mathrm{C}$
<br/><br/>
$$
\frac{6}{d t}=-k[72-22]=-k 50
$$
<br/><... | mcq | jee-main-2023-online-25th-january-morning-shift | 12,321 |
8bqfBOBoQsbI3gud | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respectively. A solid ball, made of a material of density $${\rho _3}$$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $${\rho _1}$$ , $$... | [{"identifier": "A", "content": "$${\\rho _3} < {\\rho _1} < \\rho {}_2$$ "}, {"identifier": "B", "content": "$${\\rho _1} > {\\rho _3} > \\rho {}_2$$"}, {"identifier": "C", "content": "$${\\rho _1} < {\\rho _2} < \\rho {}_3$$ "}, {"identifier": "D", "content": "$${\\rho _1} < {\\rho _3} < \\rho... | ["D"] | null | From the figure it is clear that liquid $$1$$ floats on liquid $$2.$$ The lighter liquid floats over heavier liquid. Therefore we can conclude that $${\rho _1} < {\rho _2}$$
<p>Also $${\rho _3} < {\rho _2}$$ otherwise the ball would have sink to the bottom of the jar. </p>
<p>Also $${\rho _3} > {\rho _1}$$ oth... | mcq | aieee-2008 | 12,323 |
y1q04uyfTyOvaIHY | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho _{oil}}$$ and $${\rho _{water}}$$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, ... | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266445/exam_images/hlt3yvlrb6whyarcfs3x.webp\" loading=\"lazy\" alt=\"AIEEE 2010 Physics - Properties of Matter Question 227 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"qu... | ["B"] | null | Oil will float on water so, $$(2)$$ or $$(4)$$ is the correct option, But density of ball is more than that of oil, hence it will sinkin oil. | mcq | aieee-2010 | 12,324 |
SYDzQFOHq2tXWOE9 | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pr... | [{"identifier": "A", "content": "$$16$$ $$cm$$ "}, {"identifier": "B", "content": "$$22$$ $$cm$$ "}, {"identifier": "C", "content": "$$38$$ $$cm$$ "}, {"identifier": "D", "content": "$$6$$ $$cm$$ "}] | ["A"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/7lKI8TVgGY0YnryKE/eWXbZOVFv2xKXsiKcVMfMo1pyYB9C/4v9DNQxaTwPnYdcQS4mpq7/image.svg" loading="lazy" alt="JEE Main 2014 (Offline) Physics - Properties of Matter Question 233 English Explanation">
Length of the air column above mercury in the tube is,
<br>$$P... | mcq | jee-main-2014-offline | 12,326 |
Z2L9kxnG55X4OCQb | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha $$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is :
<img src="da... | [{"identifier": "A", "content": "$${{1 + \\sin \\,\\alpha } \\over {1 - \\sin \\,\\alpha }}$$ "}, {"identifier": "B", "content": "$${{1 + \\cos \\,\\alpha } \\over {1 - \\cos \\,\\alpha }}$$ "}, {"identifier": "C", "content": "$${{1 + \\tan \\,\\alpha } \\over {1 - \\tan \\,\\alpha }}$$ "}, {"identifier": "D", "content... | ["C"] | null | Pressure at interface A must be same from both the sides to be in equilibrium.
<br><img class="question-image" src="https://imagex.cdn.examgoal.net/VQHrqGARCO0pXbT0b/dbADRNPX3jg2vhM7pGtLy9D2Z6ck0/VDPkg4C7bYwqG7KFXtOce7/image.svg" loading="lazy" alt="JEE Main 2014 (Offline) Physics - Properties of Matter Question 223 E... | mcq | jee-main-2014-offline | 12,327 |
e0y6LNdqEoe1snKqV7SEa | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho _1}$$ and $${\rho _2}$$ $$\left( {{\rho _1} > {\rho _2}} \right),$$ fill half the circle. The angle $$\theta $$ between the radius vector passing through the common in... | [{"identifier": "A", "content": "$$\\theta = {\\tan ^{ - 1}}\\pi \\left( {{{{\\rho _1}} \\over {{\\rho _2}}}} \\right)$$"}, {"identifier": "B", "content": "$$\\theta = {\\tan ^{ - 1}}{\\pi \\over 2}\\left( {{{{\\rho _1}} \\over {{\\rho _2}}}} \\right)$$"}, {"identifier": "C", "content": "$$\\theta = {\\tan ^{ - 1}}... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267311/exam_images/udqvewgalrcwps5nuxug.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2018 (Online) 15th April Morning Slot Physics - Properties of Matter Question 220 English Explanation">
<br><b... | mcq | jee-main-2018-online-15th-april-morning-slot | 12,328 |
5uTPayYBrNWKq8LoJTfsO | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) : | [{"identifier": "A", "content": "11.2 m"}, {"identifier": "B", "content": "8.7 m"}, {"identifier": "C", "content": "9.5 m"}, {"identifier": "D", "content": "10.5 m"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l32ml357/5dca2a81-d08c-4d40-b9a0-9245556266ee/28a7dfb0-d1bc-11ec-9218-efb2cf12c71b/file-1l32ml358.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l32ml357/5dca2a81-d08c-4d40-b9a0-9245556266ee/28a7dfb0-d1bc-11ec-9218-efb2cf12c71b... | mcq | jee-main-2018-online-15th-april-evening-slot | 12,329 |
41V8MqKuvjHMKW4MdOPFy | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be : | [{"identifier": "A", "content": "2.0 "}, {"identifier": "B", "content": "1.2"}, {"identifier": "C", "content": "0.1"}, {"identifier": "D", "content": "0.4"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266696/exam_images/yrsxnxrpr5bg7m39gw3x.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th January Evening Slot Physics - Properties of Matter Question 204 English Explanation">
<br>... | mcq | jee-main-2019-online-12th-january-evening-slot | 12,330 |
xsVgjVvBsUzi3gIJvQ3rsa0w2w9jx7hxz6e | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | The number density of molecules of a gas depends on their distance r from the origin as, $$n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$$.
Then the total number of molecules is proportional to : | [{"identifier": "A", "content": "$${n_0}{\\alpha ^{ - 3/4}}$$"}, {"identifier": "B", "content": "$${n_0}{\\alpha ^{ - 3}}$$"}, {"identifier": "C", "content": "$${n_0}{\\alpha ^{1/4}}$$"}, {"identifier": "D", "content": "$$\\sqrt {{n_0}} {\\alpha ^{1/2}}$$"}] | ["A"] | null | Lets take an element hollow sphere of thickness dr
<br><br>Vol. of element dV = 4$$\pi $$r<sup>2</sup>dr
<br><br>Total number of molecules,
<br><br>N = $$\int\limits_0^\infty {n\,dV} $$
<br><br> = $$\int\limits_0^\infty {{n_0}{e^{ - \alpha {r^4}}}\,4\pi {r^2}dr} $$
<br><br>Let $${{e^{ - \alpha {r^4}}}}$$ = t ........... | mcq | jee-main-2019-online-12th-april-evening-slot | 12,331 |
BLERHm2bQTRneJf51y3rsa0w2w9jwziirp5 | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A submarine experiences a pressure of 5.05 × 10<sup>6</sup>
Pa at a depth of d<sub>1</sub> in a sea. When it goes further to a depth
of d<sub>2</sub>, it experiences a pressure of 8.08 × 10<sup>6</sup>
Pa. Then d<sub>2</sub> –d<sub>1</sub> is approximately (density of water = 10<sup>3</sup>
kg/m<sup>3</sup>
and acce... | [{"identifier": "A", "content": "600 m"}, {"identifier": "B", "content": "400 m"}, {"identifier": "C", "content": "300 m"}, {"identifier": "D", "content": "500 m"}] | ["C"] | null | <p>The pressure experienced by a submarine at a certain depth in the sea is given by the formula:</p>
<p>$P = \rho g h$</p>
<p>where:</p>
<ul>
<li>$P$ is the pressure</li>
<li>$\rho$ is the density of the fluid (sea water in this case)</li>
<li>$g$ is the acceleration due to gravity</li>
<li>$h$ is the height (or depth... | mcq | jee-main-2019-online-10th-april-evening-slot | 12,333 |
MSQZ5Ki0MybDlwwK8bgrV | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A simple pendulum oscillating in air has period
T. The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is
1/16 th of the material of the bob.
If the bob is inside liquid all the time, its period
of oscillation in this liquid is : | [{"identifier": "A", "content": "$$2T\\sqrt {{1 \\over {10}}} $$"}, {"identifier": "B", "content": "$$4T\\sqrt {{1 \\over {14}}} $$"}, {"identifier": "C", "content": "$$4T\\sqrt {{1 \\over {15}}} $$"}, {"identifier": "D", "content": "$$2T\\sqrt {{1 \\over {14}}} $$"}] | ["C"] | null | For a simple pendulum T = $$2\pi \sqrt {{L \over {{g_{err}}}}} $$<br><br>
Situation 1: when pendulum is in air $$ \to $$ g<sub>eff</sub> = g<br>
Situation 2:when pendulum is in liquid<br>
$$ \to $$ g<sub>eff</sub> = $$\left( {1 - {{{\rho _{liquid}}} \over {{\rho _{body}}}}} \right) = g\left( {1 - {1 \over {16}}} \right... | mcq | jee-main-2019-online-9th-april-morning-slot | 12,335 |
oUZOjCPR8sYeAJ8zSh5mM | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A liquid of density $$\rho $$ is coming out of a hose pipe of radius a with horizontal speed $$\upsilon $$ and hits a mesh. 50% of
the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be : | [{"identifier": "A", "content": "$${3 \\over 4}\\rho {v^2}$$"}, {"identifier": "B", "content": "$${1 \\over 4}\\rho {v^2}$$"}, {"identifier": "C", "content": "$${1 \\over 2}\\rho {v^2}$$"}, {"identifier": "D", "content": "$$\\rho {v^2}$$"}] | ["A"] | null | Momentum per second carried by liquid per second is $$\rho $$av<sup>2</sup>
<br><br>net force due to reflected liquid = 2$$ \times $$$$\left[ {{1 \over 4}\rho a{v^2}} \right]$$
<br><br>net force due to stopped liquid = $${{1 \over 4}\rho a{v^2}}$$
<br><br>Total force = $${{3 \over 4}\rho a{v^2}}$$
<br><br>net pressure ... | mcq | jee-main-2019-online-11th-january-morning-slot | 12,337 |
PVvrWFVoYt1GSjaJx9jgy2xukff4ggcd | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A hollow spherical shell at outer radius R floats
just submerged under the water surface. The
inner radius of the shell is r. If the specific
gravity of the shell material is $${{27} \over 8}$$ w.r.t water,
the value of r is : | [{"identifier": "A", "content": "$${{2} \\over 3}$$R"}, {"identifier": "B", "content": "$${{4} \\over 9}$$R"}, {"identifier": "C", "content": "$${{1} \\over 3}$$R"}, {"identifier": "D", "content": "$${{8} \\over 9}$$R"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263516/exam_images/nxqnqtgefdnkn2nfwye1.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 5th September Morning Slot Physics - Properties of Matter Question 171 English Explanation">
<br>$... | mcq | jee-main-2020-online-5th-september-morning-slot | 12,338 |
D6cuCx03Gk4g2jMh80jgy2xukf6hhz70 | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s<sup>–2</sup>. The density of water is
1 gm cm<sup>–3</sup> and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980
cm/s<sup>2</sup>). | [{"identifier": "A", "content": "1.52 gm"}, {"identifier": "B", "content": "4.51 gm"}, {"identifier": "C", "content": "3.15 gm"}, {"identifier": "D", "content": "4.15 gm"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267167/exam_images/w2ygcb315rrgr1bpwwa7.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 4th September Morning Slot Physics - Properties of Matter Question 174 English Explanation">
<br><... | mcq | jee-main-2020-online-4th-september-morning-slot | 12,339 |
5qA8VP0uw25yF897537k9k2k5guwz42 | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | Consider a solid sphere of radius R and mass
density<br/> $$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$ , $$0 < r \le R$$<br/> The
minimum density of a liquid in which it will
float is : | [{"identifier": "A", "content": "$${{2{\\rho _0}} \\over 3}$$"}, {"identifier": "B", "content": "$${{2{\\rho _0}} \\over 5}$$"}, {"identifier": "C", "content": "$${{{\\rho _0}} \\over 5}$$"}, {"identifier": "D", "content": "$${{{\\rho _0}} \\over 3}$$"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264022/exam_images/v1wrvn3pphz0japnird0.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Morning Slot Physics - Properties of Matter Question 186 English Explanation">
<br>Mas... | mcq | jee-main-2020-online-8th-january-morning-slot | 12,341 |
rdr5ehPwmHkZTaQrTE7k9k2k5hgvgio | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | Two liquids of densities $${\rho _1}$$ an $${\rho _2}$$ ($${\rho _2}$$ = 2$${\rho _1}$$) are
filled up behind a square wall of side 10 m as
shown in figure. Each liquid has a height of
5 m. The ratio of the forces due to these liquids
exerted on upper part MN to that at the lower part
NO is (Assume that the liquids are... | [{"identifier": "A", "content": "1/3"}, {"identifier": "B", "content": "1/2"}, {"identifier": "C", "content": "1/4"}, {"identifier": "D", "content": "2/3"}] | ["C"] | null | Force F<sub>1</sub> on MN = $${{\rho gh} \over 2} \times A$$
<br><br>Force F<sub>2</sub> on NO = $$\left( {\rho gh + {{2\rho gh} \over 2}} \right) \times A$$
<br><br>$${{{F_1}} \over {{F_2}}} = {1 \over 4}$$ | mcq | jee-main-2020-online-8th-january-evening-slot | 12,342 |
tZ4xOxTSc85rJR1oGM1kmhna31e | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | The pressure acting on a submarine is 3 $$\times$$ 10<sup>5</sup> Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : <br/><br/>(Assume that atmospheric pressure is 1 $$\times$$ 10<sup>5</sup> Pa density of water is 10<sup>3</sup> kg m<sup>$$-$$3</s... | [{"identifier": "A", "content": "$${{200} \\over 5}$$%"}, {"identifier": "B", "content": "$${{200} \\over 3}$$%"}, {"identifier": "C", "content": "$${{3} \\over 200}$$%"}, {"identifier": "D", "content": "$${{5} \\over 200}$$%"}] | ["B"] | null | P = P<sub>0</sub> + h$$\rho$$g = 3 $$\times$$ 10<sup>5</sup> Pa<br><br>$$ \Rightarrow $$ h$$\rho$$g = 3 $$\times$$ 10<sup>5</sup> $$-$$ 1 $$\times$$ 10<sup>5</sup><br><br>$$ \Rightarrow $$ h$$\rho$$g = 2 $$\times$$ 10<sup>5</sup><br><br>$$ \therefore $$ 2h$$\rho$$g = 4 $$\times$$ 10<sup>5</sup><br><br>$$ \therefore $$ ... | mcq | jee-main-2021-online-16th-march-morning-shift | 12,344 |
5vK8rlj4pgurq9vk4Y1kmkbvztj | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm<sup>$$-$$3</sup> and g = 9.8 ms<sup>$$-$$2</sup>] | [{"identifier": "A", "content": "1.44 $$\\times$$ 10<sup>7</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "B", "content": "1.44 $$\\times$$ 10<sup>9</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "C", "content": "1.96 $$\\times$$ 10<sup>7</sup> Nm<sup>$$-$$2</sup>"}, {"identifier": "D", "content": "2.26 $$\\times$$ 10<sup>9<... | ["B"] | null | $$\beta = {{\Delta p} \over {{{\Delta V} \over V}}}$$<br><br>$$ \Rightarrow $$ $$\beta = {{\Delta \rho gh} \over {{{\Delta V} \over V}}} = {{1000 \times 9.8 \times 2 \times {{10}^3}} \over {{{1.36} \over {100}}}}$$<br><br>$$ \Rightarrow $$ $$\beta$$ = 1.44 $$\times$$ 10<sup>9</sup> N/m<sup>2</sup> | mcq | jee-main-2021-online-17th-march-evening-shift | 12,345 |
1krywddxa | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :<br/><br/><img src="data:image... | [{"identifier": "A", "content": "$${A \\over {2a}}$$"}, {"identifier": "B", "content": "None of these"}, {"identifier": "C", "content": "$${{2a} \\over A}$$"}, {"identifier": "D", "content": "$${{a} \\over A}$$"}] | ["C"] | null | For no sliding <br><br>f $$\ge$$ $$\rho$$av<sup>2</sup><br><br>$$\mu$$mg $$\ge$$ $$\rho$$av<sup>2</sup><br><br>$$\mu$$$$\rho$$Ahg $$\ge$$ $$\rho$$a2gh<br><br>$$\mu \ge {{2a} \over A}$$<br><br>Option (3) | mcq | jee-main-2021-online-27th-july-morning-shift | 12,346 |
1l6f4dsu7 | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $$7.5 \times 10^{-4}$$ Ncm<sup>$$-$$1</sup>. The radius of drop in $$\mathrm{cm}$$ will be :</p>
<p>(g = 10 ms<sup>$$-$$2</sup>)</p> | [{"identifier": "A", "content": "$$\n\\frac{15}{\\sqrt{(2 \\rho-\\sigma)}}\n$$"}, {"identifier": "B", "content": "$$\\frac{15}{\\sqrt{(\\rho-\\sigma)}}$$"}, {"identifier": "C", "content": "$$\\frac{3}{2 \\sqrt{(\\rho-\\sigma)}}$$"}, {"identifier": "D", "content": "$$\\frac{3}{20 \\sqrt{(2 \\rho-\\sigma)}}$$"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lf8jmexo/d19ae171-e39c-40d6-889a-4bddd868eeee/dea105c0-c28f-11ed-979c-cdbdd295ffc4/file-1lf8jmexp.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lf8jmexo/d19ae171-e39c-40d6-889a-4bddd868eeee/dea105c0-c28f-11ed-979c-cdbdd295ffc4/fi... | mcq | jee-main-2022-online-25th-july-evening-shift | 12,347 |
1l6jh308s | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>Two cylindrical vessels of equal cross-sectional area $$16 \mathrm{~cm}^{2}$$ contain water upto heights $$100 \mathrm{~cm}$$ and $$150 \mathrm{~cm}$$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, densit... | [{"identifier": "A", "content": "0.25 J"}, {"identifier": "B", "content": "1 J"}, {"identifier": "C", "content": "8 J"}, {"identifier": "D", "content": "12 J"}] | ["B"] | null | <p>$$A = 16 \times {10^{ - 4}}$$ m<sup>2</sup></p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6xtieam/d201f0d2-be5e-46cd-9d09-4eab63f03c0c/3003afe0-1e48-11ed-9c61-4529b721806b/file-1l6xtiean.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6xtieam/d201f0d2-be5e-46cd-9d0... | mcq | jee-main-2022-online-27th-july-morning-shift | 12,348 |
1l6rip7xz | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>The velocity of a small ball of mass $$0.3 \mathrm{~g}$$ and density $$8 \mathrm{~g} / \mathrm{cc}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $$1.3 \mathrm{~g} / \mathrm{cc}$$, then the value of viscous force acting on the ball will be $$x \ti... | [] | null | 25 | $F_{\mathrm{V}}+F_B=m g(v=$ constant $)$
<br/><br/>$F_V=m g-F_B$
<br/><br/>$=\rho_{\mathrm{B}} \mathrm{Vg}-\rho_{\mathrm{L}} \mathrm{Vg}$
<br/><br/>$=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{Vg}$
<br/><br/>$=(8-1.3) \times 10^{+3} \times \frac{0.3 \times 10^{-3}}{8 \times 10^3} \times 10$
<br/><br/>$=\f... | integer | jee-main-2022-online-29th-july-evening-shift | 12,351 |
1lgxwszgi | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>Given below are two statements:</p>
<p>Statement I : Pressure in a reservoir of water is same at all points at the same level of water.</p>
<p>Statement II : The pressure applied to enclosed water is transmitted in all directions equally.</p>
<p>In the light of the above statements, choose the correct answer from th... | [{"identifier": "A", "content": "Both Statement I and Statement II are false"}, {"identifier": "B", "content": "Statement I is false but Statement II is true"}, {"identifier": "C", "content": "Statement I is true but Statement II is false"}, {"identifier": "D", "content": "Both Statement I and Statement II are true"}] | ["D"] | null | <p><b>Statement I</b>: Pressure in a reservoir of water is same at all points at the same level of water.</p>
<p>This statement is true. According to the principle of fluid statics, in a body of static fluid, the pressure is the same at all points at the same horizontal level. This is because the pressure at any point ... | mcq | jee-main-2023-online-10th-april-morning-shift | 12,353 |
jaoe38c1lsc4okne | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>If average depth of an ocean is $$4000 \mathrm{~m}$$ and the bulk modulus of water is $$2 \times 10^9 \mathrm{~Nm}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______ (Given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \rh... | [] | null | 2 | <p>$$\begin{aligned}
& \mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)} \\
& -\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)=\frac{\rho \mathrm{gh}}{\mathrm{B}}=\frac{1000 \times 10 \times 4000}{2 \times 10^9} \\
& =2 \times 10^{-2}[-\mathrm{ve} \text { sign represent compressi... | integer | jee-main-2024-online-27th-january-morning-shift | 12,355 |
jaoe38c1lse6sd4s | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.</p>
<p>(Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)</p> | [] | null | 18 | <p>$$\begin{aligned}
& \beta=\frac{-\Delta \mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}} \\
& \Delta \mathrm{P}=-\beta \frac{\Delta \mathrm{V}}{\mathrm{V}} \\
& \rho \mathrm{gh}=-\beta \frac{\Delta \mathrm{V}}{\mathrm{V}} \\
& 10^3 \times 10 \times \mathrm{h}=-9 \times 10^8 \times\left(-\frac{0.02}{100}\right) \\
&... | integer | jee-main-2024-online-31st-january-morning-shift | 12,356 |
luy9cm0f | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac{D}{d}$$, if it just floats on water in a tank is :</p> | [{"identifier": "A", "content": "$$\\left(\\frac{\\sigma-2}{\\sigma+2}\\right)^{1 / 3}$$\n"}, {"identifier": "B", "content": "$$\\left(\\frac{\\sigma+1}{\\sigma-1}\\right)^{1 / 3}$$\n"}, {"identifier": "C", "content": "$$\\left(\\frac{\\sigma-1}{\\sigma}\\right)^{1 / 3}$$\n"}, {"identifier": "D", "content": "$$\\left(\... | ["D"] | null | <p>To solve this problem, we consider the buoyancy and weight force acting on the sphere. For the sphere to just float on water, the weight of the water displaced by the sphere must be equal to the weight of the sphere. The volume of water displaced by the sphere is equivalent to the outer volume of the sphere minus th... | mcq | jee-main-2024-online-9th-april-morning-shift | 12,357 |
lv2erj3y | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p>Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.</p>
<p>(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 ... | [] | null | 177 | <p>$$\begin{aligned}
F & =\left(p_0+\rho g h\right) A \\
& =\left(10^5+1.36 \times 10^4 \times 10 \times \frac{3}{10}\right) \frac{22}{7}\left(\frac{2}{100}\right)^2 \\
& =177 \mathrm{~N}
\end{aligned}$$</p> | integer | jee-main-2024-online-4th-april-evening-shift | 12,358 |
lv9s2smu | physics | properties-of-matter | pressure,-density,-pascal's-law-and-archimede's-principle | <p><img src="data:image/png;base64,UklGRp4RAABXRUJQVlA4IJIRAAAw5QCdASoAA78BP4G82WO2L6ymoPD64sAwCWlu/CAlWpBAf1ln8OyNB9/1a/43+I/Pf53XGbG/Ff9V2fc8v9r3276LxeoK3UMx5h40c7Ml//+nH92//vrfDVXDqGEWrh1DCLVw6hhFq4dQwi1beam/ATht1TOSws0myP0nTw83kS+4WaTZH6Tp4ebyIvOzWQLNJs2JqKws0myP0nTw83kS+4WaTZH6Tp4ebxwIv+Q3ejEup41FUD639jfuW1FxDFbI/... | [] | null | 1000 | <p>$$\frac{F_1}{A_1}=\frac{F_2}{A_2}\quad$$ (By Pascal's law)</p>
<p>$$\begin{aligned}
\Rightarrow F_1 & =10\left(\frac{14^2}{1.4^2}\right) \\
& =10 \times 100 \\
& =1000 \mathrm{~N}
\end{aligned}$$</p> | integer | jee-main-2024-online-5th-april-evening-shift | 12,360 |
S6j9UNcdkfJJNxbl | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is | [{"identifier": "A", "content": "$${{{S^2}} \\over {2Y}}$$ "}, {"identifier": "B", "content": "$$2{S^2}Y$$ "}, {"identifier": "C", "content": "$${S \\over {2Y}}$$ "}, {"identifier": "D", "content": "$${{2Y} \\over {{S^2}}}$$ "}] | ["A"] | null | Energy stored per unit volume of wire,
<br><br>$$E = {1 \over 2} \times \,stress\, \times \,strain$$
<br><br>$$\therefore$$ $$E = {1 \over 2} \times \,stress\, \times \,{{stress} \over Y} = {1 \over 2}{{{S^2}} \over Y}$$
<br><br>[ As Young's modulus(Y) = $${{Stress} \over {Strain}}$$
<br><br>$$\therefore$$ Strain = $$... | mcq | aieee-2005 | 12,361 |
kCA7h1B83EeX5iDX | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by $${100^ \circ }C$$ is:
(For steel Young's modulus is $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ and coefficient of thermal expansion is $$1.1 \times {10^{ - 5}}\,{K^{ - 1}}$$... | [{"identifier": "A", "content": "$$2.2 \\times {10^8}\\,\\,Pa$$"}, {"identifier": "B", "content": "$$2.2 \\times {10^9}\\,\\,Pa$$"}, {"identifier": "C", "content": "$$2.2 \\times {10^7}\\,\\,Pa$$"}, {"identifier": "D", "content": "$$2.2 \\times {10^6}\\,\\,Pa$$"}] | ["A"] | null | Young's modulus $$Y = {{stress} \over {strain}}$$
<br>$$stress = Y \times strain$$
<br>$$Stress$$ in steel wire $$=$$ Applied $$pressure$$
<br>$$Pressure$$ $$=$$ $$stress$$ $$=$$ $$Y \times \,strain$$
<br>$$Strain = {{\Delta L} \over L} = \alpha \Delta T$$ (As length is constant)
<br>$$ = 2 \times {10^{11}} \times 1.1... | mcq | jee-main-2014-offline | 12,362 |
IgaETLABE4gqyEzTmMyzl | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | A boy's catapult is made of rubber cord which
is 42 cm long, with 6 mm diameter of
cross-section and of negligible mass. The boy
keeps a stone weighing 0.02kg on it and
stretches the cord by 20 cm by applying a
constant force. When released, the stone flies
off with a velocity of 20 ms<sup>–1</sup>. Neglect the
change ... | [{"identifier": "A", "content": "10<sup>4</sup> Nm<sup>\u20132</sup>"}, {"identifier": "B", "content": "10<sup>6</sup> Nm<sup>\u20132</sup>"}, {"identifier": "C", "content": "10<sup>8</sup> Nm<sup>\u20132</sup>"}, {"identifier": "D", "content": "10<sup>3</sup> Nm<sup>\u20132</sup>"}] | ["B"] | null | <p>When rubber cord is stretched, then it stores potential energy and when released, this potential energy is given to the stone as kinetic energy.</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l331bzfx/2b2d459c-4efc-4c94-8c34-111615e91e02/d47394e0-d1f5-11ec-b83f-ebfea682138a/file-1l331bzfy.pn... | mcq | jee-main-2019-online-8th-april-morning-slot | 12,364 |
mUVu0LQl0pp0OSnnBE7k9k2k5lcepvz | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | Two steel wires having same length are
suspended from a ceiling under the same load.
If the ratio of their energy stored per unit
volume is 1 : 4, the ratio of their diameters is: | [{"identifier": "A", "content": "1 : 2"}, {"identifier": "B", "content": "2 : 1"}, {"identifier": "C", "content": "$$1:\\sqrt 2 $$"}, {"identifier": "D", "content": "$$\\sqrt 2 :1$$"}] | ["D"] | null | $${{du} \over {dv}}$$ = $${1 \over 2}$$ $$ \times $$ stress × strain
<br><br>= $${1 \over 2}{F \over A} \times {F \over {AY}}$$ $$ \propto $$ $${1 \over {{A^2}}}$$ $$ \propto $$ $${1 \over {{d^4}}}$$
<br><br>$${{du} \over {dv}}$$ = $${1 \over 4}$$
<br><br>$$ \Rightarrow $$ $${\left( {{{{d_1}} \over {{d_2}}}} \right)^4}... | mcq | jee-main-2020-online-9th-january-evening-slot | 12,366 |
1kryyvsag | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10<sup>$$-$$6</sup> m<sup>2</sup> stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.<br/><br/>(Young's modulus of rubber = 0.5 $$\times$$ 10<sup>9</sup> N/m<sup>2</sup>) | [] | null | 20 | By energy conservation<br><br>$${1 \over 2}.{{YA} \over L}.{x^2} = {1 \over 2}m{v^2}$$<br><br>$${{0.5 \times {{10}^9} \times {{10}^{ - 6}} \times {{(0.04)}^2}} \over {0.1}} = {{20} \over {1000}}{v^2}$$<br><br>$$\therefore$$ $${v^2} = 400$$<br><br>$$v = 20$$ m/s | integer | jee-main-2021-online-27th-july-morning-shift | 12,367 |
1l58cgt7j | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | <p>The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $$\times$$ 10<sup>$$-$$4</sup> is __________ kJ/m<sup>3</sup>. Assume that material is elastic upto the linear strain of 5 $$\times$$ 10<sup>$$-$$4</sup>.</p>
<p><img src="data:i... | [] | null | 25 | <p>slope of strain $$-$$ stress curve given by $$ = {{{{10}^{ - 10}}} \over {20}}$$</p>
<p>for strain of $$5 \times {10^{ - 4}}$$ stress is given by</p>
<p>$$5 \times {10^{ - 4}} = {{{{10}^{ - 10}}} \over {20}} \times $$ stress</p>
<p>stress = 10<sup>8</sup> N/m<sup>2</sup></p>
<p>Energy density $$ = {1 \over 2}$$ $$\t... | integer | jee-main-2022-online-26th-june-morning-shift | 12,369 |
1l6jjig8p | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | <p>A square aluminum (shear modulus is $$25 \times 10^{9}\, \mathrm{Nm}^{-2}$$) slab of side $$60 \mathrm{~cm}$$ and thickness $$15 \mathrm{~cm}$$ is subjected to a shearing force (on its narrow face) of $$18.0 \times 10^{4}$$ $$\mathrm{N}$$. The lower edge is riveted to the floor. The displacement of the upper edge is... | [] | null | 48 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6xtk1od/f549401c-ab0e-4f41-9766-8136a9924459/5de300f0-1e48-11ed-9c61-4529b721806b/file-1l6xtk1of.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6xtk1od/f549401c-ab0e-4f41-9766-8136a9924459/5de300f0-1e48-11ed-9c61-4529b721806b... | integer | jee-main-2022-online-27th-july-morning-shift | 12,370 |
1ldujonrt | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | <p>As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$$^\circ$$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to ... | [] | null | 5 | Given, Length, $L=62.8 \mathrm{~cm}$
<br><br>diameter, $d=4 \mathrm{~mm}$
<br><br>radius, $r=2 \mathrm{~mm}$
<br><br>$y=x \times 10^4 \mathrm{~N} / \mathrm{m}^2$
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1ldvawm1x/d082b6c8-213a-44b7-b37c-b1dc8b8aeb36/603c3d50-a77b-11ed-a5e3-ff739bca566a... | integer | jee-main-2023-online-25th-january-morning-shift | 12,372 |
1lgq3rfvr | physics | properties-of-matter | stress-strain-curve,-thermal-stress-and-elastic-pe | <p>The elastic potential energy stored in a steel wire of length $$20 \mathrm{~m}$$ stretched through $$2 \mathrm{~cm}$$ is $$80 \mathrm{~J}$$. The cross sectional area of the wire is __________ $$\mathrm{mm}^{2}$$.</p>
<p>$$\left(\right.$$ Given, $$\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$$</p> | [] | null | 40 | Given, energy per unit volume = $$\frac{1}{2} \times \text{stress} \times \text{strain}$$
<br/><br/>
The stress can be given as $$\text{stress} = Y \times \text{strain}$$, where Y is the Young's modulus.
<br/><br/>
The energy stored in the wire can be written as:
<br/><br/>
$$\text{Energy} = \frac{1}{2} \times \text{st... | integer | jee-main-2023-online-13th-april-morning-shift | 12,373 |
KmsyQpLUo41ombZ4 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | If two soap bubbles of different radii are connected by a tube | [{"identifier": "A", "content": "air flows from the smaller bubble to the bigger "}, {"identifier": "B", "content": "air flows from bigger bubble to the smaller bubble till the sizes are interchanged "}, {"identifier": "C", "content": "air flows from the bigger bubble to the smaller bubble till the sizes become equal"}... | ["A"] | null | Pressure inside the bubble, P $$ = {p_0} + {{4T} \over R}$$
<br><br>So $$P \propto {1 \over R}$$ where R is the radius of the bubble. It means pressure inside a smaller bubble is greater than the inside of a bigger bubble.
<br><br>So when two bubbles are connected by a tube, air will flow from smaller bubble to bigger... | mcq | aieee-2004 | 12,374 |
RochDBwLIGJ7tkF5 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be | [{"identifier": "A", "content": "$$10$$ $$cm$$"}, {"identifier": "B", "content": "$$8$$ $$cm$$ "}, {"identifier": "C", "content": "$$20$$ $$cm$$ "}, {"identifier": "D", "content": "$$4$$ $$cm$$"}] | ["C"] | null | In freely falling elevator $$g$$ = 0
<br><br>Water fills the tube entirely in gravity less condition. Hence, length of water column in the capillary tube is 20 cm. | mcq | aieee-2005 | 12,375 |
Bp681fyqk3nkIjzr | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265177/exam_images/njpfb9vxruzie1fcbhgv.webp\" loading=\"lazy\" alt=\"AIEEE 2008 Physics - Properties of Matter Question 229 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"qu... | ["C"] | null | In case of water, the meniscus shape is concave upwards. Also according to ascent formula $$h = {{2T\,\cos \,\theta } \over {r\rho g}}$$
<p>The surface tension $$(I)$$ of soap solution is less than water. Therefore rise of soap solution in the capillary tube is less as compared to water. As in the case of water. the me... | mcq | aieee-2008 | 12,376 |
0hM3R0dHuhcC0OME | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times {10^{ - 2}}\,\,N$$ (see figure). The length of the slider is $$30$$ $$cm$$ and its weight negligible. The surface tension of the liquid film is
<img src="data:image/png;base64,UklGRo4VAABXRUJQVlA4IIIVAABwewCdASpvAZw... | [{"identifier": "A", "content": "$$0.0125\\,\\,N{m^{ - 1}}$$ "}, {"identifier": "B", "content": "$$0.1\\,\\,N{m^{ - 1}}$$ "}, {"identifier": "C", "content": "$$0.05\\,\\,N{m^{ - 1}}$$ "}, {"identifier": "D", "content": "$$0.025\\,\\,N{m^{ - 1}}$$ "}] | ["D"] | null | At equilibrium,
<br>$$2Tl = mg$$
<br>$$T = {{mg} \over {2l}} = {{1.5 \times {{10}^{ - 2}}} \over {2 \times 30 \times {{10}^{ - 2}}}} = {{1.5} \over {60}}$$
<br>$$ = 0.025\,N/m = 0.025Nm$$ | mcq | aieee-2012 | 12,378 |
h2ksQg8poRTZ5YzJ2h8du | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P<sub>2</sub> be the pressure inside the inner bubble and P<sub>0</sub>, the pressure outside the outer bubble. Radius of another bubble with pressure difference P<sub>2</sub> $$-$$ P<sub>0</sub> between its insi... | [{"identifier": "A", "content": "12 cm"}, {"identifier": "B", "content": "2.4 cm"}, {"identifier": "C", "content": "6 cm"}, {"identifier": "D", "content": "4.8 cm"}] | ["B"] | null | Pressure difference inside the inner bubble,
<br><br>p<sub>2</sub> $$-$$ p<sub>1</sub> = $${{4T} \over {{r_2}}}$$b . . . . . (1)
<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265191/exam_images/i9oqrogzlywcz6aml4pc.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" ... | mcq | jee-main-2018-online-16th-april-morning-slot | 12,379 |
cUGhY12csjJJqT3L5I6fk | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | If 'M' is the mass of water that rises in a capillary
tube of radius 'r', then mass of water which will
rise in a capillary tube of radius '2r' is : | [{"identifier": "A", "content": "M"}, {"identifier": "B", "content": "4M"}, {"identifier": "C", "content": "M/2"}, {"identifier": "D", "content": "2M"}] | ["D"] | null | Height of liquid rise in capillary tube $$h = {{2T\,\cos {\theta _c}} \over {\rho rg}}$$<br><br>
$$ \Rightarrow h \propto {1 \over r}$$<br><br>
When radius becomes double height become half<br><br>
$$ \therefore $$ $${h^{'}} = {h \over 2}$$<br>
Now, M = $$\pi $$r<sup>2</sup>h × $$\rho $$ and M<sup>'</sup> = $$\pi $$(2r... | mcq | jee-main-2019-online-9th-april-morning-slot | 12,380 |
RKRHNK8a2zSJnr3btU18hoxe66ijvztv1aj | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | The ratio of surface tensions of mercury and
water is given to be 7.5 while the ratio of thier
densities is 13.6. Their contact angles, with
glass, are close to 135° and 0°, respectively. It
is observed that mercury gets depressed by an
amount h in a capillary tube of radius r<sub>1</sub>, while
water rises by the same... | [{"identifier": "A", "content": "2/5"}, {"identifier": "B", "content": "2/3"}, {"identifier": "C", "content": "3/5"}, {"identifier": "D", "content": "4/5"}] | ["A"] | null | $$h = {{2{S_1}\cos \theta } \over {{r_1}{\rho _1}g}}$$<br>
<br>
$$h = {{2{s_2}\cos {\theta _2}} \over {{r_2}{\rho _2}g}}$$<br>
<br>
$$ \Rightarrow {{{r_1}} \over {{r_2}}} = {2 \over 5}$$ | mcq | jee-main-2019-online-10th-april-morning-slot | 12,381 |
XVXC9Lo2BAsuewvfurjgy2xukexyd31v | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A capillary tube made of glass of radius 0.15
mm is dipped vertically in a beaker filled with
methylene iodide (surface tension = 0.05 Nm<sup>–1</sup>,
density = 667 kg m<sup>–3</sup>) which rises to height h in
the tube. It is observed that the two tangents
drawn from liquid-glass interfaces (from opp.
sides of the ca... | [{"identifier": "A", "content": "0.049 m"}, {"identifier": "B", "content": "0.087 m"}, {"identifier": "C", "content": "0.137 m"}, {"identifier": "D", "content": "0.172 m"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267003/exam_images/qldja1xrnkukoe5cofob.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 2nd September Evening Slot Physics - Properties of Matter Question 179 English Explanation">
<br><... | mcq | jee-main-2020-online-2nd-september-evening-slot | 12,383 |
WCbuQ6qzqUleoGJsCRjgy2xukf16b0fg | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their
volumes is : | [{"identifier": "A", "content": "4 : 1"}, {"identifier": "B", "content": "8 : 1"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "0.8 : 1"}] | ["B"] | null | $${P_{in}} = {P_0} + {{4T} \over {{R_1}}}$$<br><br>
$$ \Rightarrow 1.01 = 1 + {{4T} \over {{R_1}}}$$<br><br>
$$ \Rightarrow {{4T} \over {{R_1}}} = 0.01$$<br><br>
$$1.02 = 1 + {{4T} \over {{R_2}}}$$<br><br>
$$ \Rightarrow {{4T} \over {{R_2}}} = 0.02$$<br><br>
$$ \therefore {{{R_2}} \over {{R_1}}} = {1 \over 2}$$<br><br>... | mcq | jee-main-2020-online-3rd-september-morning-slot | 12,384 |
JzEmdvixnuKKnFjwmV1klthg4fm | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be : | [{"identifier": "A", "content": "$${{2T} \\over J}\\left( {{1 \\over r} - {1 \\over R}} \\right)$$"}, {"identifier": "B", "content": "$${{3T} \\over J}\\left( {{1 \\over r} - {1 \\over R}} \\right)$$"}, {"identifier": "C", "content": "$${{3T} \\over rJ}$$"}, {"identifier": "D", "content": "$${{2T} \\over rJ}$$"}] | ["B"] | null | R is the radius of bigger drop.<br><br>r is the radius of n water drops.<br><br>Water drops are combined to make bigger drop.<br><br>So,<br><br>Volume of n drops = volume of bigger drop<br><br>$$n\left( {{4 \over 3}\pi {r^3}} \right) = {4 \over 3}\pi {R^3}$$<br><br>$$ \Rightarrow $$ $$R = r{n^{1/3}} \Rightarrow n = {\l... | mcq | jee-main-2021-online-26th-february-morning-slot | 12,386 |
fUNNYvnWQKSB9ierCT1kmkbzfai | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm<sup>3</sup> of oleic acid per cm<sup>3</sup> of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm<sup>2</sup> by considering 100 spherical drops of radius $${\left( {... | [] | null | 25 | 4t<sub>T</sub> = 100 $$ \times $$ $${4 \over 3}\pi {r^3}$$
<br><br>= $$100 \times {4 \over 3}\pi \times {3 \over {40\pi }} \times {10^{ - 9}}$$
<br><br>= 10<sup>-8</sup> cm<sup>3</sup>
<br><br>$$ \Rightarrow $$ t<sub>T</sub> = 25 $$ \times $$ 10<sup>-10</sup> cm
<br><br>= 25 $$ \times $$ 10<sup>-12</sup> m
<br><br>t<s... | integer | jee-main-2021-online-17th-march-evening-shift | 12,388 |
1krqdlzso | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is : | [{"identifier": "A", "content": "$${2^{{1 \\over 3}}}:1$$"}, {"identifier": "B", "content": "$$1:{2^{{1 \\over 3}}}$$"}, {"identifier": "C", "content": "2 : 1"}, {"identifier": "D", "content": "1 : 2"}] | ["A"] | null | <p>The volume of a sphere is given by $\frac{4}{3}\pi R^3$.</p>
<p>So the volume of the two small mercury drops each of radius $R$ is $2\times \frac{4}{3}\pi R^3$.</p>
<p>When they coalesce to form a larger drop, the volume is conserved. So, the volume of the larger drop is also $2\times \frac{4}{3}\pi R^3$.</p>
<p>Let... | mcq | jee-main-2021-online-20th-july-evening-shift | 12,389 |
1krw9i5jn | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | Two spherical soap bubbles of radii r<sub>1</sub> and r<sub>2</sub> in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to : | [{"identifier": "A", "content": "$${{{r_1}{r_2}} \\over {{r_1} + {r_2}}}$$"}, {"identifier": "B", "content": "$$\\sqrt {{r_1}{r_2}} $$"}, {"identifier": "C", "content": "$$\\sqrt {r_1^2 + r_2^2} $$"}, {"identifier": "D", "content": "$${{{r_1} + {r_2}} \\over 2}$$"}] | ["C"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264810/exam_images/pbazk2rxbfqfoyz6hzu8.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266520/exam_images/wdmxwmwazowgekrxcnpk.webp"><img src="https://res.c... | mcq | jee-main-2021-online-25th-july-evening-shift | 12,390 |
1kta95ui1 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $$\times$$ 10<sup>$$-$$2</sup> Nm<sup>$$-$$1</sup>, angle of contact = 0, g = ... | [{"identifier": "A", "content": "3.62 mm"}, {"identifier": "B", "content": "2.19 mm"}, {"identifier": "C", "content": "5.34 mm"}, {"identifier": "D", "content": "4.97 mm"}] | ["B"] | null | Image<br><br>We have, P<sub>A</sub> = P<sub>B</sub>. [Points A & B at same horizontal level]<br><br>$$\therefore$$ $${P_{atm}} - {{2T} \over {{r_1}}} + \rho g(x + \Delta h) = {P_{atm}} - {{2T} \over {{r_2}}} + \rho gx$$<br><br>$$\therefore$$ $$\rho g\Delta h = 2T\left[ {{1 \over {{r_1}}} - {1 \over {{r_2}}}} \right... | mcq | jee-main-2021-online-26th-august-morning-shift | 12,391 |
1ktaggvkf | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm. | [] | null | 2 | Image<br><br>Excess pressure inside the smaller soap bubble<br><br>$$\Delta P = {{4S} \over {{r_1}}} + {{4S} \over {{r_2}}}$$ .... (i)<br><br>The excess pressure inside equivalent soap bubble<br><br>$$\Delta P = {{4S} \over {{R_{eq}}}}$$ ....... (ii)<br><br>From (i) & (ii)<br><br>$${{4S} \over {{R_{eq}}}} = {{4S} \... | integer | jee-main-2021-online-26th-august-morning-shift | 12,392 |
1l5690g3o | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :</p> | [{"identifier": "A", "content": "2.8 $$\\times$$ 10<sup>$$-$$4</sup> J"}, {"identifier": "B", "content": "1.5 $$\\times$$ 10<sup>$$-$$3</sup> J"}, {"identifier": "C", "content": "1.9 $$\\times$$ 10<sup>$$-$$4</sup> J"}, {"identifier": "D", "content": "9.4 $$\\times$$ 10<sup>$$-$$5</sup> J"}] | ["A"] | null | <p>$$r' = {r \over 4}$$</p>
<p>$$ \Rightarrow \Delta E = T(\Delta S)$$</p>
<p>$$ = T \times 4\pi (nr{'^2} - {r^2}),\,n = 64$$</p>
<p>$$ = T \times 4\pi \times (4 - 1){r^2}$$</p>
<p>$$ \Rightarrow \Delta E = 0.075 \times 4 \times 3.142(3) \times {10^{ - 4}}\,$$ J</p>
<p>$$ = 2.8 \times {10^{ - 4}}$$ J</p> | mcq | jee-main-2022-online-28th-june-morning-shift | 12,393 |
1l5w3gurb | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>The excess pressure inside a liquid drop is 500 Nm<sup>$$-$$2</sup>. If the radius of the drop is 2 mm, the surface tension of liquid is x $$\times$$ 10<sup>$$-$$3</sup> Nm<sup>$$-$$1</sup>. The value of x is _____________.</p> | [] | null | 500 | $\mathrm{P}=\mathrm{P}_{0}+\frac{2 T}{R} $
<br/><br/>$\Rightarrow P-P_{0}=\frac{2 T}{R}$
<br/><br/>$$
\begin{aligned}
&500=\frac{2 \times T}{2 \times 10^{-3}} \\\\
&T=500 \times 10^{-3} \\\\
&\text { So, } x=500
\end{aligned}
$$ | integer | jee-main-2022-online-30th-june-morning-shift | 12,394 |
1l6gmwos9 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A water drop of radius $$1 \mathrm{~cm}$$ is broken into 729 equal droplets. If surface tension of water is 75 dyne/ $$\mathrm{cm}$$, then the gain in surface energy upto first decimal place will be :</p>
<p>(Given $$\pi=3.14$$ )</p> | [{"identifier": "A", "content": "$$8.5 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "B", "content": "$$8.2 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "C", "content": "$$7.5 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "D", "content": "$$5.3 \\times 10^{-4} \\mathrm{~J}$$"}] | ["C"] | null | <p>$$729 \times {4 \over 3}\pi {r^3} = {4 \over 3}\pi {R^3}$$</p>
<p>$$ \Rightarrow R = 9r$$ ........ (1)</p>
<p>$$\Delta U = S \times \Delta A$$ ..... (2)</p>
<p>$$ \Rightarrow \Delta U = S \times \{ - 4\pi {R^2} + 729 \times 4\pi {r^2}\} $$</p>
<p>$$ = S \times 4\pi \{ 729{r^2} - 81{r^2}\} $$</p>
<p>$$ = 7.5 \times ... | mcq | jee-main-2022-online-26th-july-morning-shift | 12,395 |
1l6kohktn | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___________.</p> | [] | null | 2 | <p>$${{4T} \over {{R_1}}} + {{4T} \over {{R_2}}} = {{4T} \over r}$$</p>
<p>$$ \Rightarrow {1 \over r} = {1 \over 3} + {1 \over 6} \Rightarrow r = 2$$ cm</p> | integer | jee-main-2022-online-27th-july-evening-shift | 12,396 |
1ldogkwe0 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A mercury drop of radius $$10^{-3}~\mathrm{m}$$ is broken into 125 equal size droplets. Surface tension of mercury is $$0.45~\mathrm{Nm}^{-1}$$. The gain in surface energy is :</p> | [{"identifier": "A", "content": "$$28\\times10^{-5}~\\mathrm{J}$$"}, {"identifier": "B", "content": "$$17.5\\times10^{-5}~\\mathrm{J}$$"}, {"identifier": "C", "content": "$$5\\times10^{-5}~\\mathrm{J}$$"}, {"identifier": "D", "content": "$$2.26\\times10^{-5}~\\mathrm{J}$$"}] | ["D"] | null | Initial surface energy $=0.45 \times 4 \pi\left(10^{-3}\right)^2$
<br/><br/>$$
\begin{aligned}
& \frac{4}{3} \pi\left(10^{-3}\right)^3=125 \times \frac{4 \pi}{3} R_{\text {new }}^3 \\\\
\therefore & 10^{-3}=5 R_{\text {new }} \\\\
\therefore & R_{\text {new }}=\frac{10^{-3}}{5} \mathrm{~m}
\end{aligned}
$$
<br/><br/>So... | mcq | jee-main-2023-online-1st-february-morning-shift | 12,398 |
1ldpm86x9 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>If 1000 droplets of water of surface tension $$0.07 \mathrm{~N} / \mathrm{m}$$, having same radius $$1 \mathrm{~mm}$$ each, combine to from a single drop. In the process the released surface energy is :-</p>
<p>$$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$$</p> | [{"identifier": "A", "content": "$$7 .92 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "B", "content": "$$7 .92 \\times 10^{-6} \\mathrm{~J}$$"}, {"identifier": "C", "content": "$$8 .8 \\times 10^{-5} \\mathrm{~J}$$"}, {"identifier": "D", "content": "$$9 .68 \\times 10^{-4} \\mathrm{~J}$$"}] | ["A"] | null | $1000 \times \frac{4 \pi}{3}(1)^{3}=\frac{4 \pi}{3} \mathrm{R}^{3}$
<br/><br/>$\mathrm{R}=10 \mathrm{~mm}$
<br/><br/>$\mathrm{T} \times 1000 \times 4 \pi\left(10^{-3}\right)^{2}-\mathrm{T} \times 4 \pi\left(10 \times 10^{-3}\right)^{2}=\Delta \mathrm{E}$
<br/><br/>$$ \Rightarrow $$ $\Delta \mathrm{E}=4 \times \pi \t... | mcq | jee-main-2023-online-31st-january-morning-shift | 12,399 |
1ldr0udq1 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mathrm{~cm}$$. If the tube is dipped in a similar manner in another liquid $$\mathrm{B}$$ of surface tension and density double the values of liquid $$\mathrm{A}$$, the height of liquid column raised ... | [{"identifier": "A", "content": "0.05"}, {"identifier": "B", "content": "0.20"}, {"identifier": "C", "content": "0.5"}, {"identifier": "D", "content": "0.10"}] | ["A"] | null | <p>height of capillary rise $$ = {{2s\cos \theta } \over {\rho gR}}$$</p>
<p>When in A 5 cm $$ = {{2{s_A}\cos \theta } \over {{\rho _A}gR}}$$</p>
<p>When in B $$h = {{2{s_B}\cos \theta } \over {{\rho _B}gR}}$$</p>
<p>$${s_B} = 2{s_A}$$ and $${\rho _B} = 2{\rho _A}$$</p>
<p>$$h = {{2 \times 2{s_A} \times \cos \theta } \... | mcq | jee-main-2023-online-30th-january-morning-shift | 12,400 |
1ldso6nz9 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Surface tension of a soap bubble is $$2.0 \times 10^{-2} \mathrm{Nm}^{-1}$$. Work done to increase the radius of soap bubble from $$3.5 \mathrm{~cm}$$ to $$7 \mathrm{~cm}$$ will be:</p>
<p>Take $$\left[\pi=\frac{22}{7}\right]$$</p> | [{"identifier": "A", "content": "$$18 .48 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "B", "content": "$$5.76 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "C", "content": "$$0.72 \\times 10^{-4} \\mathrm{~J}$$"}, {"identifier": "D", "content": "$$9.24 \\times 10^{-4} \\mathrm{~J}$$"}] | ["A"] | null | Surface area of soap bubble $=2 \times 4 \pi \mathrm{R}^{2}$ Work done $=$ change in surface energy $\times \mathrm{T}_{\mathrm{S}}$
<br/><br/>
$=\mathrm{T}_{\mathrm{S}} \times 8 \pi \times\left(\mathrm{R}_{2}^{2}-\mathrm{R}_{1}^{2}\right)$
<br/><br/>
$=2 \times 10^{-2} \times 8 \times \frac{22}{7} \times 49 \times \fr... | mcq | jee-main-2023-online-29th-january-morning-shift | 12,401 |
1ldu03enh | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A spherical drop of liquid splits into 1000 identical spherical drops. If u$$_\mathrm{i}$$ is the surface energy of the original drop and u$$_\mathrm{f}$$ is the total surface energy of the resulting drops, the (ignoring evaporation), $${{{u_f}} \over {{u_i}}} = \left( {{{10} \over x}} \right)$$. Then value of x is ... | [] | null | 1 | Surface Tension $=\mathrm{T}$<br/><br/>
$\mathrm{R}$ : Radius of bigger drop<br/><br/>
$\mathrm{r}$ : Radius of smaller drop<br/><br/>
Volume will remain same<br/><br/>
$\frac{4}{3} \pi R^3=1000 \times \frac{4}{3} \pi r^3$<br/><br/>
$\mathrm{R}=10 \mathrm{r}$<br/><br/>
$\mathrm{u}_{\mathrm{i}}=\mathrm{T} \cdot 4 \pi \m... | integer | jee-main-2023-online-25th-january-evening-shift | 12,402 |
1ldugs59u | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Match List I with List II</p>
<p><style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;bo... | [{"identifier": "A", "content": "A-IV, B-III, C-I, D-II"}, {"identifier": "B", "content": "A-IV, B-III, C-II, D-I"}, {"identifier": "C", "content": "A-I, B-I, C-III, D-IV"}, {"identifier": "D", "content": "A-III, B-IV, C-I, D-II"}] | ["A"] | null | $$
\begin{aligned}
\text { (A) } \text { Surface Tension }=\frac{\mathrm{F}}{\ell} & =\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}}=\mathrm{ML}^{0} \mathrm{~T}^{-2} \\\\
& =\mathrm{kg\,s}^{-2}(\mathrm{IV})
\end{aligned}
$$<br/><br/>
$$
\begin{aligned}
& \text { (B) Pressure }=\frac{F}{\mathrm{~A}}=\frac{\mathrm{MLT}^{-2}}{\mat... | mcq | jee-main-2023-online-25th-january-morning-shift | 12,403 |
1ldwrq11a | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension (s) of the liquid as $$\nu=r^a\rho^b s^c$$. The values of a, b and c respectively are</p> | [{"identifier": "A", "content": "$$\\left( {{3 \\over 2},{1 \\over 2}, - {1 \\over 2}} \\right)$$"}, {"identifier": "B", "content": "$$\\left( { - {3 \\over 2}, - {1 \\over 2},{1 \\over 2}} \\right)$$"}, {"identifier": "C", "content": "$$\\left( {{3 \\over 2}, - {1 \\over 2},{1 \\over 2}} \\right)$$"}, {"identifier": "... | ["B"] | null | $[v]=\left[\mathrm{T}^{-1}\right]$
<br/><br/>
$$
\begin{aligned}
& {[r]=\mathrm{L} \quad[s]=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}}\right]} \\\\
& {[\rho]=\left[\frac{\mathrm{M}}{\mathrm{L}^{3}}\right]=\left[\mathrm{ML}^{-3}\right]} \\\\
& \Rightarrow v=r^{a} \rho^{b} \mathrm{~s}^{c} \\\\
& \Rightarrow \mathrm{T}^{... | mcq | jee-main-2023-online-24th-january-evening-shift | 12,404 |
lgnz4koo | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | There is an air bubble of radius $1.0 \mathrm{~mm}$ in a liquid of surface tension $0.075~ \mathrm{Nm}^{-1}$ and density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ at a depth of $10 \mathrm{~cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ $... | [] | null | 1150 | We can use the Young-Laplace equation to find the difference in pressure inside and outside the air bubble due to surface tension:
<br/><br/>
$\Delta P = 2 \frac{T}{R}$
<br/><br/>
where $\Delta P$ is the pressure difference, $T$ is the surface tension, and $R$ is the radius of the bubble.
<br/><br/>
Plugging in the giv... | integer | jee-main-2023-online-15th-april-morning-shift | 12,405 |
1lgq1n52c | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p><img src="data:image/png;base64,UklGRpoMAABXRUJQVlA4II4MAABQlgCdASoAAwMBP4G+22K2MK4mJDJp+sAwCWlu+F9JAzCM7Ovn9dO9xzh1IfBP+v3hOwTwDwKUXXoFH16U1P/3Mf//q5+/xr4j96jjq8ghYgbb7ToU+x0/LhQ2uNp7A232nQp9jp5822caErimF7jmvMVGm+Sa/qfG09gbb7ToU+x0/LhQ2uNp7A232nPn+AiNIV50gZZKBrIuSSOWIvmzdFj0p9jp+XChtcbT2BtvtOhT7HT8sftJw7+b+ItbFTXYF... | [{"identifier": "A", "content": "$$27 \\mathrm{~Pa}$$"}, {"identifier": "B", "content": "$$175 \\mathrm{~Pa}$$"}, {"identifier": "C", "content": "$$135 \\mathrm{~Pa}$$"}, {"identifier": "D", "content": "$$36 \\mathrm{~Pa}$$"}] | ["B"] | null | From continuity theorem $\mathrm{A}_1 \mathrm{~V}_1=\mathrm{A}_2 \mathrm{~V}_2$<br/><br/>
$$
\begin{aligned}
& 1.5 \times \mathrm{V}_1=25 \times 10^{-2} \times 60 \\\\
& \mathrm{~V}_1=\frac{25 \times 60 \times 10^{-2} \times 10}{1.5} \\\\
& \mathrm{~V}_1=10 \mathrm{~cm} / \mathrm{s}
\end{aligned}
$$<br/><br/>
By Bernou... | mcq | jee-main-2023-online-13th-april-morning-shift | 12,406 |
1lgrjt3pi | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are $$10 \mathrm{~cm}^{2}$$ and $$5 \mathrm{~cm}^{2}$$ and pressure drop across its length is $$3 ~\mathrm{Nm}^{-2}$$. The rate of flow of glycerin... | [] | null | 4 | <p>We can use the Bernoulli equation and continuity equation to solve this problem. The Bernoulli equation is given by:</p>
<p>$$P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2$$</p>
<p>The continuity equation is given by:</p>
<p>$$A_1 v_1 = A_2 v_2$$</p>
<p>From the given data, we have:</p>
<p>$$P_1 - P_2 ... | integer | jee-main-2023-online-12th-april-morning-shift | 12,407 |
1lgswvd5r | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Eight equal drops of water are falling through air with a steady speed of $$10 \mathrm{~cm} / \mathrm{s}$$. If the drops coalesce, the new velocity is:-</p> | [{"identifier": "A", "content": "$$40 \\mathrm{~cm} / \\mathrm{s}$$"}, {"identifier": "B", "content": "$$16 \\mathrm{~cm} / \\mathrm{s}$$"}, {"identifier": "C", "content": "$$10 \\mathrm{~cm} / \\mathrm{s}$$"}, {"identifier": "D", "content": "$$5 \\mathrm{~cm} / \\mathrm{s}$$"}] | ["A"] | null | In this problem, we need to consider the terminal velocity of the droplets, which is reached when the gravitational force is balanced by the drag force acting on the droplet. Terminal velocity is related to the square of the droplet's radius.
<br/><br/>
The relationship between the terminal velocity (v) and the radius ... | mcq | jee-main-2023-online-11th-april-evening-shift | 12,408 |
1lh00rp0f | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>An air bubble of volume $$1 \mathrm{~cm}^{3}$$ rises from the bottom of a lake $$40 \mathrm{~m}$$ deep to the surface at a temperature of $$12^{\circ} \mathrm{C}$$. The atmospheric pressure is $$1 \times 10^{5} \mathrm{~Pa}$$ the density of water is $$1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{... | [{"identifier": "A", "content": "$$4 \\mathrm{~cm}^{3}$$"}, {"identifier": "B", "content": "$$3 \\mathrm{~cm}^{3}$$"}, {"identifier": "C", "content": "$$2 \\mathrm{~cm}^{3}$$"}, {"identifier": "D", "content": "$$5 \\mathrm{~cm}^{3}$$"}] | ["D"] | null | <p>The volume of the air bubble changes due to the change in pressure as it rises from the bottom of the lake to the surface. We can use Boyle's Law to calculate the change in volume, which states that the product of pressure and volume is constant for a given mass of confined gas held at a constant temperature:</p... | mcq | jee-main-2023-online-8th-april-morning-shift | 12,410 |
1lh02n5xi | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>An air bubble of diameter $$6 \mathrm{~mm}$$ rises steadily through a solution of density $$1750 \mathrm{~kg} / \mathrm{m}^{3}$$ at the rate of $$0.35 \mathrm{~cm} / \mathrm{s}$$. The co-efficient of viscosity of the solution (neglect density of air) is ___________ Pas (given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ).<... | [] | null | 10 | <p>The terminal velocity of a small spherical object moving under the action of gravity through a fluid medium is given by Stokes' Law, which is stated as:</p>
<p>$v = \frac{2}{9} \frac{r^2 g (\rho_p - \rho_f)}{\eta}$,</p>
<p>where:</p>
<ul>
<li>$v$ is the velocity of the object (in this case, the air bubble),</li>... | integer | jee-main-2023-online-8th-april-morning-shift | 12,411 |
lsamqzfu | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become : | [{"identifier": "A", "content": "$\\frac{1}{100}$ th"}, {"identifier": "B", "content": "$\\frac{1}{10}$ th"}, {"identifier": "C", "content": "100 times"}, {"identifier": "D", "content": "10 times"}] | ["B"] | null | <p>To answer this question, we need to understand the relationship between the surface area of the droplets and the surface energy involved.</p>
<p>Surface energy is directly proportional to the surface area of the liquid. The surface energy, $$ E $$, for a droplet is given by:</p>
<p>$$ E = \gamma \times A $$</p>
<p>W... | mcq | jee-main-2024-online-1st-february-evening-shift | 12,412 |
jaoe38c1lsc2ulli | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Given below are two statements :</p>
<p>Statement (I) :Viscosity of gases is greater than that of liquids.</p>
<p>Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.</p>
<p>In the light of the above statements, choose the most appropriate answer from the options given ... | [{"identifier": "A", "content": "Statement I is correct but statement II is incorrect\n"}, {"identifier": "B", "content": "Statement I is incorrect but Statement II is correct\n"}, {"identifier": "C", "content": "Both Statement I and Statement II are incorrect\n"}, {"identifier": "D", "content": "Both Statement I and S... | ["B"] | null | <p>Gases have less viscosity.</p>
<p>Due to insoluble impurities like detergent surface tension decreases</p> | mcq | jee-main-2024-online-27th-january-morning-shift | 12,413 |
jaoe38c1lsf1inbp | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Given below are two statements:</p>
<p>Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.</p>
<p>Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will... | [{"identifier": "A", "content": "Both Statement I and Statement II are false\n"}, {"identifier": "B", "content": "Both Statement I and Statement II are true\n"}, {"identifier": "C", "content": "Statement I is true but Statement II is false\n"}, {"identifier": "D", "content": "Statement I is false but Statement II is tr... | ["C"] | null | <p>Surface tension will be less as temperature increases</p>
<p>$$\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\rho \mathrm{gr}}$$</p>
<p>Height of capillary rise will be smaller in hot water and larger in cold water.</p> | mcq | jee-main-2024-online-29th-january-morning-shift | 12,414 |
jaoe38c1lsflhccd | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A small liquid drop of radius $$R$$ is divided into 27 identical liquid drops. If the surface tension is $$T$$, then the work done in the process will be:</p> | [{"identifier": "A", "content": "$$4 \\pi \\mathrm{R}^2 \\mathrm{~T}$$\n"}, {"identifier": "B", "content": "$$8 \\pi R^2 \\mathrm{~T}$$\n"}, {"identifier": "C", "content": "$$\\frac{1}{8} \\pi R^2 T$$\n"}, {"identifier": "D", "content": "$$3 \\pi R^2 \\mathrm{~T}$$"}] | ["B"] | null | <p>Volume constant</p>
<p>$$\begin{aligned}
& \frac{4}{3} \pi R^3=27 \times \frac{4}{3} \times \pi r^3 \\
& R^3=27 r^3 \\
& R=3 r \\
& r=\frac{R}{3} \\
& r^2=\frac{R^2}{9}
\end{aligned}$$</p>
<p>$$\begin{aligned}
& \text { Work done }=T . \Delta A \\
& =27 T\left(4 \pi r^2\right)-T 4 \pi R^2 \\
& =27 T 4 \pi \frac{R^2}... | mcq | jee-main-2024-online-29th-january-evening-shift | 12,415 |
luxwe3fy | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:</p> | [{"identifier": "A", "content": "$$1: 9$$\n"}, {"identifier": "B", "content": "$$1: 27$$\n"}, {"identifier": "C", "content": "$$1: 81$$\n"}, {"identifier": "D", "content": "$$1: 3$$"}] | ["B"] | null | <p>To find the ratio between the volumes of the first and the second soap bubble, we need to understand the relation between the excess pressure inside a soap bubble and its volume.</p>
<p>The excess pressure ($P$) inside a soap bubble is given by the formula:</p>
<p>$$P = \frac{4T}{r}$$</p>
<p>where $T$ is the surf... | mcq | jee-main-2024-online-9th-april-evening-shift | 12,417 |
lv0vy08y | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it further. If surface tension of soap solution is 40 dyne/$$\mathrm{cm}$$ then the new radius is ________ cm Take $$(\pi=\frac{22}{7})$$.</p> | [] | null | 7 | <p>$$\begin{aligned}
& \Delta W=8 \pi\left(R_2^2-R_1^2\right) T \\
& 36960=8 \times \frac{22}{7} \times 40\left(R_2^2-\frac{49}{4}\right) \\
& R_2=7 \mathrm{~cm}
\end{aligned}$$</p> | integer | jee-main-2024-online-4th-april-morning-shift | 12,418 |
lv2es16x | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Given below are two statements :</p>
<p>Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.</p>
<p>Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.</p>
<p>In the light of the above statemen... | [{"identifier": "A", "content": "Both Statement I and Statement II are false.\n"}, {"identifier": "B", "content": "Both Statement I and Statement II are true.\n"}, {"identifier": "C", "content": "Statement I is false but Statement II is true.\n"}, {"identifier": "D", "content": "Statement I is true but Statement II is ... | ["D"] | null | <p>Option D, "Statement I is true but Statement II is false," is the correct choice. Here's an explanation for both statements:</p>
<p><strong>Statement I: True</strong></p>
<p>The contact angle between a solid and a liquid is indeed a measure of the wettability of the solid surface by the liquid. The contact angle i... | mcq | jee-main-2024-online-4th-april-evening-shift | 12,419 |
lv5gsxzs | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if ... | [] | null | 7 | <p>Let's start by understanding the problem. We need to determine the diameter of the soap bubble, given certain properties of the liquid and the soap solution.</p>
<p>The excess pressure inside a soap bubble can be calculated using the formula:</p>
<p>$$ \Delta P = \frac{4T}{r} $$</p>
<p>where:</p>
<ul>
<li>$$\De... | integer | jee-main-2024-online-8th-april-morning-shift | 12,420 |
lv7v3oh5 | physics | properties-of-matter | surface-tension,-excess-pressure-and-capillarity | <p>Given below are two statements :</p>
<p>Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $$0^{\circ}$$.</p>
<p>Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid ... | [{"identifier": "A", "content": "Statement I is true and Statement II is false\n"}, {"identifier": "B", "content": "Statement I is false but Statement II is true\n"}, {"identifier": "C", "content": "Both Statement I and Statement II are true\n"}, {"identifier": "D", "content": "Both Statement I and Statement II are fal... | ["B"] | null | <p>Both statements given above have implications relating to the phenomena of capillarity, which involves the interaction between a liquid and a solid (in this case, a capillary tube). Let's break down each statement for clarity.</p>
<p><strong>Statement I:</strong> When a capillary tube is dipped into a liquid and th... | mcq | jee-main-2024-online-5th-april-morning-shift | 12,421 |
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