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1l59m1icq | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | <p>A solid metallic cube having total surface area 24 m<sup>2</sup> is uniformly heated. If its temperature is increased by 10$$^\circ$$C, calculate the increase in volume of the cube. (Given $$\alpha$$ = 5.0 $$\times$$ 10<sup>$$-$$4</sup> $$^\circ$$C<sup>$$-$$1</sup>).</p> | [{"identifier": "A", "content": "2.4 $$\\times$$ 10<sup>6</sup> cm<sup>3</sup>"}, {"identifier": "B", "content": "1.2 $$\\times$$ 10<sup>5</sup> cm<sup>3</sup>"}, {"identifier": "C", "content": "6.0 $$\\times$$ 10<sup>4</sup> cm<sup>3</sup>"}, {"identifier": "D", "content": "4.8 $$\\times$$ 10<sup>5</sup> cm<sup>3</sup... | ["B"] | null | <p>$$6 \times {l^2} = 24$$</p>
<p>$$ \Rightarrow l = 2$$ m</p>
<p>$$\therefore$$ $${{\Delta V} \over V} = 3 \times {{\Delta l} \over l}$$</p>
<p>$$ \Rightarrow \Delta V = 3 \times (\alpha \Delta T) \times V$$</p>
<p>$$ = 3 \times 5 \times {10^{ - 4}} \times 10 \times (8)$$</p>
<p>$$ = 120 \times {10^{ - 3}}$$ m<sup>3</... | mcq | jee-main-2022-online-25th-june-evening-shift | 11,569 |
1l6dzyev1 | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | <p>A unit scale is to be prepared whose length does not change with temperature and remains $$20 \mathrm{~cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass i... | [] | null | 60 | <p>$$\Delta {L_1} = {\alpha _1}{L_1}\Delta T$$</p>
<p>$$\Delta {L_2} = {\alpha _2}{L_2}\Delta T$$</p>
<p>$${\alpha _1}{L_1} = {\alpha _2}{L_2}$$</p>
<p>$$1.2 \times {10^{ - 5}} \times {L_1} = 1.8 \times {10^{ - 5}} \times {L_2}$$</p>
<p>$${L_1} = {{1.8} \over {1.2}} \times 40 = 60$$ cm</p> | integer | jee-main-2022-online-25th-july-morning-shift | 11,570 |
ldqw3hus | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | A faulty thermometer reads $5^{\circ} \mathrm{C}$ in melting ice and $95^{\circ} \mathrm{C}$ in stream. The correct temperature on absolute scale will be __________ $\mathrm{K}$ when the faulty thermometer reads $41^{\circ} \mathrm{C}$. | [] | null | 313 | <p>Let the correct temperature be X$$^\circ$$C</p>
<p>$$ \Rightarrow {{X - 0} \over {100 - 0}} = {{41 - 5} \over {95 - 5}} \Rightarrow X = 40$$</p>
<p>$$\Rightarrow$$ Temperature is 273 + 40 K = 313 K</p> | integer | jee-main-2023-online-30th-january-evening-shift | 11,571 |
1ldtypeq4 | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | <p>The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :-</p>
<p><img src="data:image/png;base64,UklGRv4SAABXRUJQ... | [{"identifier": "A", "content": "$${{{t_P}} \\over {100}} = {{{t_Q} - 180} \\over {150}}$$"}, {"identifier": "B", "content": "$${{{t_P}} \\over {180}} - {{{t_Q} - 40} \\over {100}}$$"}, {"identifier": "C", "content": "$${{{t_Q}} \\over {150}} = {{{t_P} - 180} \\over {100}}$$"}, {"identifier": "D", "content": "$${{{t_Q}... | ["D"] | null | $$
\begin{aligned}
& \frac{\text { reading on scale }-\text { Lower fixed point }}{\text { upper fixed point-lower fixed point }}=\text { constant } \\\\
& \frac{t_P-30}{180-30}=\frac{t_Q-0}{100-0} \\\\
& \frac{t_P-30}{150}=\frac{t_Q}{100}
\end{aligned}
$$ | mcq | jee-main-2023-online-25th-january-evening-shift | 11,572 |
1lguxgj70 | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | <p>On a temperature scale '$$\mathrm{X}$$', the boiling point of water is $$65^{\circ} \mathrm{X}$$ and the freezing point is $$-15^{\circ} \mathrm{X}$$. Assume that the $$\mathrm{X}$$ scale is linear. The equivalent temperature corresponding to $$-95^{\circ} \mathrm{X}$$ on the Farenheit scale would be:</p> | [{"identifier": "A", "content": "$$-148^{\\circ} \\mathrm{F}$$"}, {"identifier": "B", "content": "$$-48^{\\circ} \\mathrm{F}$$"}, {"identifier": "C", "content": "$$-63^{\\circ} \\mathrm{F}$$"}, {"identifier": "D", "content": "$$-112^{\\circ} \\mathrm{F}$$"}] | ["A"] | null | We are given two temperature scales: the X-scale and the Celsius scale. The relationship between two linear temperature scales can be expressed as follows:
<br/><br/>
$$\frac{X - X_{\text{freeze}}}{X_{\text{boil}} - X_{\text{freeze}}} = \frac{C - C_{\text{freeze}}}{C_{\text{boil}} - C_{\text{freeze}}}$$
<br/><br/>
Here... | mcq | jee-main-2023-online-11th-april-morning-shift | 11,574 |
lv0vxt1h | physics | heat-and-thermodynamics | thermometry-and-thermal-expansion | <p>The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omega$$ and $$10 \Omega$$ respectively. After inserting in a hot bath of temperature $$400^{\circ} \mathrm{C}$$, the resistance of platinum wire is :</p> | [{"identifier": "A", "content": "10 $$\\Omega$$"}, {"identifier": "B", "content": "16 $$\\Omega$$"}, {"identifier": "C", "content": "8 $$\\Omega$$"}, {"identifier": "D", "content": "2 $$\\Omega$$"}] | ["B"] | null | <p>The resistance of a platinum resistance thermometer varies linearly with temperature. The relation can be given by:</p>
<p>$$R_t = R_0(1 + \alpha t)$$</p>
<p>where:
<ul>
<li>$$R_t$$ is the resistance at temperature $$t$$,</li><br>
<li>$$R_0$$ is the resistance at 0°C (ice point),</li><br>
<li>$$\alpha$$ is the te... | mcq | jee-main-2024-online-4th-april-morning-shift | 11,576 |
VbcbsEYA92IvPgf7 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | Which of the following parameters does not characterize the thermodynamic state of mattter? | [{"identifier": "A", "content": "Temperature "}, {"identifier": "B", "content": "Pressure "}, {"identifier": "C", "content": "Work "}, {"identifier": "D", "content": "Volume "}] | ["C"] | null | Work is a path function. The remaining three parameters are state function. | mcq | aieee-2003 | 11,577 |
RLq4YosFZvKtBtcC | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ volume $$\left( {{V_1},{V_2}} \right)$$ and pressure $$\left( {{P_1},{P_2}} \right)$$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will ... | [{"identifier": "A", "content": "$${T_1}{T_2}\\left( {{P_1}{V_1} + {P_2}{V_2}} \\right)/\\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \\right)$$"}, {"identifier": "B", "content": "$$\\left( {{T_1} + {T_2}} \\right)/2$$ "}, {"identifier": "C", "content": "$${{T_1} + {T_2}}$$ "}, {"identifier": "D", "content": "$${T_1}{T_2... | ["A"] | null | Here $$Q=0$$ and $$W=0.$$ Therefore from first law of thermodynamics $$\Delta U = Q + W = 0$$
<br>$$\therefore$$ Internal energy of the system with partition $$=$$ Internal energy of the system without partition.
<br>$${n_1}{C_v}\,{T_1} + {n_2}\,{C_v}{T_2} = \left( {{n_1} + {n_2}} \right){C_v}\,T$$
<br>$$\therefore$$ $... | mcq | aieee-2004 | 11,578 |
Jmxp9s6IgC7sI2V0 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | Which of the following statements is <b>correct</b> for any thermodynamic system ? | [{"identifier": "A", "content": "The change in entropy can never be zero"}, {"identifier": "B", "content": "Internal energy and entropy and state functions "}, {"identifier": "C", "content": "The internal energy changes in all processes "}, {"identifier": "D", "content": "The work done in an adiabatic process is always... | ["B"] | null | Internal energy and entropy are state function, they do not depend upon path taken. | mcq | aieee-2004 | 11,579 |
GVbxj9WNrUvCGbJM | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | Which of the following is <b>incorrect</b> regarding the first law of thermodynamics? | [{"identifier": "A", "content": "It is a restatement of the principle of conservation of energy"}, {"identifier": "B", "content": "It is not applicable to any cyclic process"}, {"identifier": "C", "content": "It introduces the concept of the entropy"}, {"identifier": "D", "content": "It introduces the concept of the in... | null | null | $$(b,c)$$ are wrong. As first law is applicable to a cyclic process and concept of entropy is introduced by the second law. | mcqm | aieee-2005 | 11,580 |
seRcS8mEhAdmW7ja | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delta {U_2}$$ are the changes in internal energies in the processes $$I$$ and $$II$$ respectively, then
<img src="data:image/png;base64,UklGRkYLAABXRUJQVlA4IDoLAABQWgCdASrLAVsBPm0ylkmkIqGhIRDJIIANiWlu/Hy... | [{"identifier": "A", "content": "relation between $$\\Delta {U_1}$$ and $$\\Delta {U_2}$$ can not be determined "}, {"identifier": "B", "content": "$$\\Delta {U_1} = \\Delta {U_2}$$ "}, {"identifier": "C", "content": "$$\\Delta {U_2} < \\Delta {U_1}$$ "}, {"identifier": "D", "content": "$$\\Delta {U_2} > \\Delta ... | ["B"] | null | Change in internal energy do not depend upon the path followed by the process. It only depends on initial and final states $$i.e.,$$ $$\Delta U{}_1 = \Delta {U_2}$$ | mcq | aieee-2005 | 11,581 |
hdE5LHQQ2DFLO5q2 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ $$Q=36$$ $$cal.$$ $$W$$ along the path $$ibf$$ is
<img src="data:image/png;base64,UklGRuoFAABXRUJQVlA4IN4FAABwOQCdASqrAekAPm02l0kkIqehIHZpYPANiWlu4XMl7mNwrZ4U/lfah/UPyS6... | [{"identifier": "A", "content": "$$14$$ $$cal$$"}, {"identifier": "B", "content": "$$6$$ $$cal$$ "}, {"identifier": "C", "content": "$$16$$ $$cal$$ "}, {"identifier": "D", "content": "$$66$$ $$cal$$"}] | ["B"] | null | For path iaf, $$\Delta U = Q - W = 50 - 20 = 30\,cal.$$
<br>For path ibf, $$W = Q - \Delta U = 36 - 30 = 6\,cal.$$ | mcq | aieee-2007 | 11,582 |
fcs8i3JM6xyXAx18 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | $$100g$$ of water is heated from $${30^ \circ }C$$ to $${50^ \circ }C$$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $$4184$$ $$J/kg/K$$): | [{"identifier": "A", "content": "$$8.4$$ $$kJ$$ "}, {"identifier": "B", "content": "$$84$$ $$kJ$$"}, {"identifier": "C", "content": "$$2.1$$ $$kJ$$ "}, {"identifier": "D", "content": "$$4.2$$ $$kJ$$"}] | ["A"] | null | $$\Delta U = \Delta Q = mc\Delta T$$
<br>$$ = 100 \times {10^{ - 3}} \times 4184\left( {50 - 30} \right) \approx 8.4\,kJ$$ | mcq | aieee-2011 | 11,585 |
XxHabjszhMGgkvqJRC3rsa0w2w9jx3nw01t | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the
internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60
J along the path bc. The work done by the gas along the path abc is:
<img src="data:image/png;base64,... | [{"identifier": "A", "content": "120 J"}, {"identifier": "B", "content": "130 J"}, {"identifier": "C", "content": "100 J"}, {"identifier": "D", "content": "140 J"}] | ["B"] | null | For the process (c – a), $$\Delta $$U<sub>ca</sub> = – 180 J<br><br>
For process (b – c) $$ \to $$ Isochoric (W<sub>bc</sub> = 0)<br><br>
$$ \therefore \Delta $$U = 60 J<br><br>
Heat absorbs along (a – b), Q<sub>ab</sub> = 250 J<br><br>
Also $$ \therefore \Delta$$ U<sub>cycle</sub> = 0<br><br>
$$ \therefore \Delta$$ U... | mcq | jee-main-2019-online-12th-april-morning-slot | 11,586 |
0Otom2zDGN8dI3K4V618hoxe66ijvzmyznh | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | A cylinder with fixed capacity of 67.2 lit
contains helium gas at STP. The amount of heat
needed to raise the temperature of the gas by
20°C is : [Given that R = 8.31 J mol<sup>–1</sup> K<sup>–1</sup>] | [{"identifier": "A", "content": "374 J"}, {"identifier": "B", "content": "700 J"}, {"identifier": "C", "content": "748 J"}, {"identifier": "D", "content": "350 J"}] | ["C"] | null | $$\Delta Q = n{C_v}$$ $$\Delta T = n{3 \over 2}R\Delta T$$<br><br>
$$ = \left( {{{67.2} \over {22.4}}} \right)\left( {{3 \over 2} \times 8.31} \right)\left( {20} \right)$$<br><br>
$$ \approx 748\,J$$ | mcq | jee-main-2019-online-10th-april-morning-slot | 11,587 |
S6LMZmds9WoEyNaGUt3ux | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | Following figure shows two processes A and
B for a gas. If $$\Delta $$Q<sub>A</sub> and $$\Delta $$Q<sub>B</sub> are the amount of
heat absorbed by the system in two cases, and
$$\Delta $$U<sub>A</sub> and $$\Delta $$U<sub>B</sub> are changes in internal energies,
respectively, then :
<img src="data:image/png;base64,Uk... | [{"identifier": "A", "content": "$$\\Delta $$Q<sub>A</sub> > $$\\Delta $$Q<sub>B</sub> ; $$\\Delta $$U<sub>A</sub> > $$\\Delta $$U<sub>B</sub>"}, {"identifier": "B", "content": "$$\\Delta $$Q<sub>A</sub> < $$\\Delta $$Q<sub>B</sub> ; $$\\Delta $$U<sub>A</sub> < $$\\Delta $$U<sub>B</sub>"}, {"identifier": "C... | ["C"] | null | Initial and final states for both the processes are
same,<br>
$$ \therefore $$ $$\Delta $$U<sub>A</sub> = $$\Delta $$U<sub>B</sub><br><br>
Work done during process A is greater than in
process B. Because area is more
By First law of thermodynamics<br>
$$\Delta $$Q = $$\Delta $$U + W<br>
$$ \Rightarrow $$ $$\Delta $$Q<s... | mcq | jee-main-2019-online-9th-april-morning-slot | 11,588 |
yPFnNl9HyCTpiXAvGE1klryterv | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is $${x \over {3R}}$$. Value of x is ___________. | [] | null | 3600 | $$\Delta {K_E} = \Delta U$$<br><br>$$\Delta U = n{C_v}\Delta T$$<br><br>$${1 \over 2}m{v^2} = {3 \over 2}nR\Delta T$$<br><br>$${{m{v^2}} \over {3nR}} = \Delta T$$<br><br>$${{4 \times {{(30)}^2}} \over {3 \times 1 \times R}} = \Delta T$$
<br><br>$$ \Rightarrow $$ $$\Delta T = {{1200} \over R}$$<br><br>$$ \Rightarrow $$ ... | integer | jee-main-2021-online-25th-february-morning-slot | 11,591 |
R0fjEpIjLlBYS4EGun1klunkp9k | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | 1 mole of rigid diatomic gas performs a work of $${Q \over 5}$$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $${xR \over 8}$$. The value of x is _________. [R = universal gas constant] | [] | null | 25 | From thermodynamics law:
<br><br>$$Q = \Delta U + W$$<br><br>$$Q = \Delta U + {Q \over 5}$$<br><br>$$\Delta U = {{4Q} \over 5}$$<br><br>$$n{C_v}\Delta T = {4 \over 5}nC\Delta T$$<br><br>$${5 \over 4}{C_v} = C$$<br><br>$$C = {5 \over 4}\left( {{f \over 2}} \right)R = {5 \over 4}\left( {{5 \over 2}} \right)R$$<br><br>$$C... | integer | jee-main-2021-online-26th-february-evening-slot | 11,592 |
3L4Q827tOxhWqGHdNu1kmhod4hp | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | In thermodynamics, heat and work are : | [{"identifier": "A", "content": "Path functions"}, {"identifier": "B", "content": "Point functions"}, {"identifier": "C", "content": "Extensive thermodynamics state variables"}, {"identifier": "D", "content": "Intensive thermodynamic state variables"}] | ["A"] | null | Heat and work are path function.<br><br>Heat and work depends on the path taken to reach the final state from initial state. | mcq | jee-main-2021-online-16th-march-morning-shift | 11,593 |
1ktabqj29 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $$\times$$ 10<sup>3</sup> J ? | [{"identifier": "A", "content": "2.5 $$\\times$$ 10<sup>2</sup> s"}, {"identifier": "B", "content": "4.1 $$\\times$$ 10<sup>1</sup> s"}, {"identifier": "C", "content": "2.4 $$\\times$$ 10<sup>3</sup> s"}, {"identifier": "D", "content": "2.5 $$\\times$$ 10<sup>1</sup> s"}] | ["A"] | null | $$\Delta$$Q = $$\Delta$$U + $$\Delta$$W<br><br>$${{\Delta Q} \over {\Delta t}} = {{\Delta U} \over {\Delta t}} + {{\Delta W} \over {\Delta t}}$$<br><br>$${{6000} \over {60}}{J \over {\sec }} = {{2.5 \times {{10}^3}} \over {\Delta t}} + 90$$<br><br>$$\Delta$$t = 250 sec | mcq | jee-main-2021-online-26th-august-morning-shift | 11,594 |
1l55k0pa7 | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during ... | [{"identifier": "A", "content": "20 J"}, {"identifier": "B", "content": "30 J"}, {"identifier": "C", "content": "$$-$$30 J"}, {"identifier": "D", "content": "$$-$$60 J"}] | ["B"] | null | <p>$$\Delta$$U<sub>AB</sub> = 40 J as process is isochoric.</p>
<p>$$\Delta$$U<sub>BC</sub> = + 50 (W<sub>BC</sub> = $$-$$ 50 J)</p>
<p>U<sub>C</sub> = U<sub>A</sub> + $$\Delta$$U<sub>AB</sub> + $$\Delta$$U<sub>BC</sub> = 1650</p>
<p>For CA process,</p>
<p>Q<sub>CA</sub> = $$-$$ 60 J</p>
<p>$$\Delta$$U<sub>CA</sub> + W... | mcq | jee-main-2022-online-28th-june-evening-shift | 11,595 |
1l6ntrlhg | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.</p> | [] | null | 750 | <p>$$f = 8$$</p>
<p>$$W = P\,dV = 150$$</p>
<p>$$Q = W + \Delta U$$</p>
<p>$$ = P\,dV + {f \over 2}\,PdV$$</p>
<p>$$Q = 5 \times 150 = 750\,J$$</p> | integer | jee-main-2022-online-28th-july-evening-shift | 11,596 |
1ldso98ll | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.</p>
<p>Assertion A: If $$d Q$$ and $$d W$$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $$d Q=d U-d W$$.</p>
<p>Reason R: ... | [{"identifier": "A", "content": "Both A and R are correct but R is not the correct explanation of A"}, {"identifier": "B", "content": "Both A and R are correct and R is the correct explanation of A"}, {"identifier": "C", "content": "A is correct but R is not correct"}, {"identifier": "D", "content": "A is not correct... | ["B"] | null | Heat supplied to the system $=d Q$
<br/><br/>Work done on the system $=-d W$
<br/><br/>By the first law of thermodynamics, $d Q=d U+d W$
<br/><br/>We done the work, therefore,
<br/><br/>$$
d Q=d U+(-d W) = d U-d W
$$
<br/><br/>So, both A and R are correct and R is the correct explanation
of A. | mcq | jee-main-2023-online-29th-january-morning-shift | 11,598 |
1lgux5x4q | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>$$1 \mathrm{~kg}$$ of water at $$100^{\circ} \mathrm{C}$$ is converted into steam at $$100^{\circ} \mathrm{C}$$ by boiling at atmospheric pressure. The volume of water changes from $$1.00 \times 10^{-3} \mathrm{~m}^{3}$$ as a liquid to $$1.671 \mathrm{~m}^{3}$$ as steam. The change in internal energy of the system d... | [{"identifier": "A", "content": "+ 2090 kJ"}, {"identifier": "B", "content": "$$-$$ 2426 kJ"}, {"identifier": "C", "content": "+ 2476 kJ"}, {"identifier": "D", "content": "$$-$$ 2090 kJ"}] | ["A"] | null | <p>To find the change in internal energy, we need to consider both the heat added during the process and the work done during the process.</p>
<p>First, let's calculate the heat added ($Q$) to convert 1 kg of water at 100°C into steam at 100°C using the latent heat of vaporization:</p>
<p>$$Q = m \times L$$</p>
<p>... | mcq | jee-main-2023-online-11th-april-morning-shift | 11,599 |
1lgvrk9lj | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>A gas is compressed adiabatically, which one of the following statement is NOT true.</p> | [{"identifier": "A", "content": "There is no heat supplied to the system"}, {"identifier": "B", "content": "The temperature of the gas increases."}, {"identifier": "C", "content": "There is no change in the internal energy"}, {"identifier": "D", "content": "The change in the internal energy is equal to the work done on... | ["C"] | null | <p>An adiabatic process is one in which there is no heat exchange between a system (in this case, the gas) and its surroundings. This happens because the system is perfectly insulated or the process occurs very quickly, not allowing for heat exchange. </p>
<p>Given the options:</p>
<p><b>Option A</b>: There is no heat ... | mcq | jee-main-2023-online-10th-april-evening-shift | 11,600 |
1lh24e1qg | physics | heat-and-thermodynamics | zeroth-and-first-law-of-thermodynamics | <p>A source supplies heat to a system at the rate of $$1000 \mathrm{~W}$$. If the system performs work at a rate of $$200 \mathrm{~W}$$. The rate at which internal energy of the system increases is</p> | [{"identifier": "A", "content": "600 W"}, {"identifier": "B", "content": "1200 W"}, {"identifier": "C", "content": "500 W"}, {"identifier": "D", "content": "800 W"}] | ["D"] | null | <p>The rate of increase of internal energy of a system can be found using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. </p>
<p>In this case, the heat being supplied to the system is 1000 W and the... | mcq | jee-main-2023-online-6th-april-morning-shift | 11,601 |
huSV7dTOkSwVod0A | physics | laws-of-motion | equilibrium-of-a-particle | When forces $${F_1},\,\,{F_2},\,\,{F_3}$$ are acting on a particle of mass $$m$$ such that $${F_2}$$ and $${F_3}$$ are mutually perpendicular, then the particle remains stationary. If the force $${F_1}$$ is now removed then the acceleration of the particle is | [{"identifier": "A", "content": "$${F_1}/m$$ "}, {"identifier": "B", "content": "$${F_2}{F_3}/m{F_1}$$ "}, {"identifier": "C", "content": "$$\\left( {F{}_2 - {F_3}} \\right)/m$$ "}, {"identifier": "D", "content": "$${F_2}/m$$ "}] | ["A"] | null | When $${F_1},{F_2}$$ and $${F_3}$$ are acting on a particle then the particle remains stationary. This means that the resultant of $${F_1},{F_2}$$ and $${F_3}$$ is zero. When $${F_1}$$ is removed then particle will start moving due to the force $${F_2}$$ and $${F_3}$$ in the resultant of $${F_2}$$ and $${F_3}$$ and i... | mcq | aieee-2002 | 11,602 |
RVfE4kZOI4yZXiMv | physics | laws-of-motion | equilibrium-of-a-particle | Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow v \,\,.$$ These forces are represented in magnitude and direction by the three sides of a triangle $$ABC$$. The particle will now move with velocity
<img src="data:image/png;base64,UklGRpwFAABXRUJQVlA4IJAFAACwUgCdASr4AWgBP4... | [{"identifier": "A", "content": "less than $$\\overrightarrow v \\,$$ "}, {"identifier": "B", "content": "greater than $$\\overrightarrow v \\,$$ "}, {"identifier": "C", "content": "$$\\left| v \\right|$$ in the direction of the largest force $$BC$$ "}, {"identifier": "D", "content": "$$\\overrightarrow v \\,\\,,$$ rem... | ["D"] | null | As shown in the figure, the three forces are represented by the sides of a triangle taken in the same order. So the particle will be in equilibrium under the three forces.
<br><br>Therefore the resultant force is zero.
<br><br> We know, $${\overrightarrow F_{net}} = m\overrightarrow a .$$
<br><br>$$\therefore$$ 0 = $$... | mcq | aieee-2003 | 11,603 |
h0QcVTf5Eey52BkU7eJH9 | physics | laws-of-motion | equilibrium-of-a-particle | A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45<sup>o</sup> at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms<sup>$$-$$2</sup> | [{"identifier": "A", "content": "200 N"}, {"identifier": "B", "content": "140 N"}, {"identifier": "C", "content": "70 N"}, {"identifier": "D", "content": "100 N"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266987/exam_images/vtm3gdrznaghqynj5v1r.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Evening Slot Physics - Laws of Motion Question 104 English Explanation">
<br>tan 45<... | mcq | jee-main-2019-online-9th-january-evening-slot | 11,604 |
Ds2EggdH6UVePJ9Hkq7k9k2k5fauisj | physics | laws-of-motion | equilibrium-of-a-particle | A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied
horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45<sup>o</sup>
with the vertical. Then F equal : (Take g = 10 ms<sup>–2</sup> and the rope to be massless) | [{"identifier": "A", "content": "100 N"}, {"identifier": "B", "content": "75 N"}, {"identifier": "C", "content": "90 N"}, {"identifier": "D", "content": "70 N"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266841/exam_images/crlq65aurxrs21vnmphd.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 7th January Evening Slot Physics - Laws of Motion Question 96 English Explanation">
<br>For equili... | mcq | jee-main-2020-online-7th-january-evening-slot | 11,605 |
1l56w1yc5 | physics | laws-of-motion | equilibrium-of-a-particle | <p>A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $$\theta$$ = tan<sup>$$-$$1</sup> (x $$\times$$ 10<sup>$$-$$1</sup>). The value of x is ___________... | [] | null | 3 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5ifn8rv/90d3d32a-dac1-4046-95c0-8389c80f7c13/fdddffb0-0205-11ed-aa88-69f11483e075/file-1l5ifn8rw.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5ifn8rv/90d3d32a-dac1-4046-95c0-8389c80f7c13/fdddffb0-0205-11ed-aa88-69f11483e075... | integer | jee-main-2022-online-27th-june-evening-shift | 11,607 |
1l6dzt7yp | physics | laws-of-motion | equilibrium-of-a-particle | <p>Four forces are acting at a point $$\mathrm{P}$$ in equilibrium as shown in figure. The ratio of force $$\mathrm{F}_{1}$$ to $$\mathrm{F}_{2}$$ is $$1: x$$ where $$x=$$ _____________.</p>
<p><img src="data:image/png;base64,UklGRoQPAABXRUJQVlA4IHgPAACQ/QCdASoAA90CP4G812a2LiqnoNBY+sAwCWlu4XUyzmNwvV6Z/zPqmuRWDGJf7PdIdt... | [] | null | 3 | <p>$${F_1} = \, + 2 \times {1 \over {\sqrt 2 }} - {1 \over {\sqrt 2 }} = {1 \over {\sqrt 2 }}$$</p>
<p>$${F_2} = 2 \times {1 \over {\sqrt 2 }} + {1 \over {\sqrt 2 }} = {3 \over {\sqrt 2 }}$$</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6tczvos/35122549-e4ca-4e7f-a3c1-79e6ae5ca280/7869cdd0-1b... | integer | jee-main-2022-online-25th-july-morning-shift | 11,609 |
1ldpmbrxi | physics | laws-of-motion | equilibrium-of-a-particle | <p>As shown in figure, a $$70 \mathrm{~kg}$$ garden roller is pushed with a force of $$\vec{F}=200 \mathrm{~N}$$ at an angle of $$30^{\circ}$$ with horizontal. The normal reaction on the roller is</p>
<p>(Given $$\mathrm{g=10~m~s^{-2}}$$)</p>
<p><img src="data:image/png;base64,UklGRsYMAABXRUJQVlA4ILoMAABQwQCdASoAA7UBP4... | [{"identifier": "A", "content": "800 N"}, {"identifier": "B", "content": "600 N"}, {"identifier": "C", "content": "200$$\\sqrt3$$ N"}, {"identifier": "D", "content": "800$$\\sqrt2$$ N"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1leh0u58l/63fb31bc-c340-49a5-b1ad-c6fa5edad65d/3e9fa350-b36d-11ed-b3df-835881d68206/file-1leh0u58m.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1leh0u58l/63fb31bc-c340-49a5-b1ad-c6fa5edad65d/3e9fa350-b36d-11ed-b3df-835881d68206/fi... | mcq | jee-main-2023-online-31st-january-morning-shift | 11,611 |
1lgrholky | physics | laws-of-motion | equilibrium-of-a-particle | <p>Three forces $$F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$$ are acting on a particle of mass $$5 \mathrm{~kg}$$. The forces $$\mathrm{F}_{2}$$ and $$\mathrm{F}_{3}$$ are applied perpendicularly so that particle remains at rest. If the force $$F_{1}$$ is removed, then the acceleration of... | [{"identifier": "A", "content": "$$4.8 \\mathrm{~ms}^{-2}$$"}, {"identifier": "B", "content": "$$7 \\mathrm{~ms}^{-2}$$"}, {"identifier": "C", "content": "$$2 \\mathrm{~ms}^{-2}$$"}, {"identifier": "D", "content": "$$0.5 \\mathrm{~ms}^{-2}$$"}] | ["C"] | null | <p>Since the particle is initially at rest, the net force acting on it is zero. This means that the forces $$F_1$$, $$F_2$$, and $$F_3$$ are balanced. Given that $$F_2$$ and $$F_3$$ are acting perpendicularly, we can represent the balance of forces as follows:</p>
<p>$$F_1 = \sqrt{F_2^2 + F_3^2}$$</p>
<p>We can now cal... | mcq | jee-main-2023-online-12th-april-morning-shift | 11,613 |
luyit9yv | physics | laws-of-motion | equilibrium-of-a-particle | <p>A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :</p> | [{"identifier": "A", "content": "$$W \\sin \\theta$$\n"}, {"identifier": "B", "content": "$$W$$\n"}, {"identifier": "C", "content": "$$\\frac{W}{2}$$\n"}, {"identifier": "D", "content": "$$W \\cos \\theta$$"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lw3kkcmo/b0a4be29-a404-4f5a-8303-9c7312f4b66e/508d9f00-1063-11ef-8227-3d00713a1ff8/file-1lw3kkcmp.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lw3kkcmo/b0a4be29-a404-4f5a-8303-9c7312f4b66e/508d9f00-1063-11ef-8227-3d00713a1ff8... | mcq | jee-main-2024-online-9th-april-morning-shift | 11,615 |
lv0vy1q6 | physics | laws-of-motion | equilibrium-of-a-particle | <p>Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F}_1$$ and $$\vec{F}_2$$ is $$\cos ^{-1}\left(\frac{1}{n}\right)$... | [] | null | 6 | <p>Let's denote the magnitude of the smaller force as $$F$$, hence the magnitude of the larger force is $$3F$$. The resultant force $$\vec{R}$$ is equal in magnitude to the larger force, which means $$|\vec{R}| = 3F$$. When two forces $$\vec{F}_1$$ and $$\vec{F}_2$$ act on a body, the magnitude of their resultant $$\ve... | integer | jee-main-2024-online-4th-april-morning-shift | 11,616 |
lvb29599 | physics | laws-of-motion | equilibrium-of-a-particle | <p>A body of weight $$200 \mathrm{~N}$$ is suspended from a tree branch through a chain of mass $$10 \mathrm{~kg}$$. The branch pulls the chain by a force equal to (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$) :</p> | [{"identifier": "A", "content": "300 N"}, {"identifier": "B", "content": "100 N"}, {"identifier": "C", "content": "150 N"}, {"identifier": "D", "content": "200 N"}] | ["A"] | null | <p>To determine the force that the branch pulls on the chain, we need to consider the combined weight of the body and the chain, as this is the total force that the branch must support due to gravity.</p>
<p>The weight of the body is given as $$200\, \mathrm{N}$$.</p>
<p>To find the weight of the chain, we use the fo... | mcq | jee-main-2024-online-6th-april-evening-shift | 11,617 |
XBQHMXZU6eEeK9y6 | physics | laws-of-motion | friction-force | A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$ $$s.$$ Then the coefficient of friction is | [{"identifier": "A", "content": "$$0.02$$ "}, {"identifier": "B", "content": "$$0.03$$ "}, {"identifier": "C", "content": "$$0.04$$ "}, {"identifier": "D", "content": "$$0.06$$ "}] | ["D"] | null | The retarding force is created by the frictional force.
<br><br> Given, $$u = 6m/s,\,v = 0,\,t = 10s,$$
<br><br>Retardation$$(a) = - {f \over m} = {{ - umg} \over m} = - \mu g = - 10\mu $$
<br><br>$$v = u + at$$
<br><br>$$0 = 6 - 10\mu \times 10$$
<br><br>$$\therefore$$ $$\mu = 0.06$$ | mcq | aieee-2003 | 11,618 |
6vKbAOZxuaCn3bCc | physics | laws-of-motion | friction-force | A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $$0.2$$. The weight of the block is
<img src="data:image/png;base64,UklGRhYOAABXRUJQVlA4IAoOAABQeACdASoQAkkBP4G41mU2LSwnJHBZUsAwCWlu3WBpK5/av7p/X8d4vv/rd6Lt9/+Hf... | [{"identifier": "A", "content": "$$20N$$ "}, {"identifier": "B", "content": "$$50N$$ "}, {"identifier": "C", "content": "$$100N$$ "}, {"identifier": "D", "content": "$$2N$$ "}] | ["D"] | null | Assume weight of the block = $$W$$ and friction force = $$f$$ = $$\mu N$$
<br><br>For the block to remain stationary with the wall, weight of the block should balanced by the force of friction.
<br><br> $$\therefore$$ $$f=W$$
<br><br>$$ \Rightarrow $$ $$\mu N = W$$
<br><br>$$ \Rightarrow $$ $$W$$ = 0.2 $$ \times $$ 10... | mcq | aieee-2003 | 11,619 |
1f9VUaOzkDjf1d7B | physics | laws-of-motion | friction-force | A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of static friction between the block and the plane is $$0.8.$$ If the frictionless force on the block is $$10$$ $$N,$$ the mass of the block (in $$kg$$) is $$\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)... | [{"identifier": "A", "content": "$$1.6$$ "}, {"identifier": "B", "content": "$$4.0$$ "}, {"identifier": "C", "content": "$$2.0$$"}, {"identifier": "D", "content": "$$2.5$$ "}] | ["C"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265812/exam_images/js1076hqs4f78y88jfy8.webp" loading="lazy" alt="AIEEE 2004 Physics - Laws of Motion Question 123 English Explanation">
<br>For equilibrum of block,
<br><br>$$mg\,\,\sin \theta = {f_s}\,\,$$
<br><br>$$ \Rightarrow ... | mcq | aieee-2004 | 11,620 |
rtT5xB5de04AZlEZ | physics | laws-of-motion | friction-force | A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to slide is $$'n'$$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is | [{"identifier": "A", "content": "$${\\mu _k} = \\sqrt {1 - {1 \\over {{n^2}}}} $$ "}, {"identifier": "B", "content": "$${\\mu _k} = 1 - {1 \\over {{n^2}}}$$ "}, {"identifier": "C", "content": "$${\\mu _k} = \\sqrt {1 - {1 \\over {{n^2}}}} $$ "}, {"identifier": "D", "content": "$${\\mu _s} = 1 - {1 \\over {{n^2}}}$$ "}] | ["B"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265074/exam_images/qfvtqjmgutbpwe3mydhn.webp" loading="lazy" alt="AIEEE 2005 Physics - Laws of Motion Question 122 English Explanation 1">
<br>For smooth surface,
<br><br>$$d = {1 \over 2}\left( {g\,\sin \,\theta } \right)t_1^2,$$
<... | mcq | aieee-2005 | 11,621 |
BddVGW1uYyT66w17 | physics | laws-of-motion | friction-force | A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = {{{x^3}} \over 6}.$$ If the coefficient of friction is $$0.5,$$ the maximum height above the ground at which the block can be placed without slipping is: | [{"identifier": "A", "content": "$${1 \\over 6}m$$ "}, {"identifier": "B", "content": "$${2 \\over 3}m$$ "}, {"identifier": "C", "content": "$${1 \\over 3}m$$ "}, {"identifier": "D", "content": "$${1 \\over 2}m$$ "}] | ["A"] | null | At limiting equilibrium, $$\mu = \tan \theta $$
<br><br>Equation of the surface,
<br><br>$$y = {{{x^3}} \over 6}$$
<br><br>Slope, $$\tan \theta = \mu = {{dy} \over {dx}} = {{{x^2}} \over 2}$$
<br><br><img class="question-image" src="https://imagex.cdn.examgoal.net/pO4ydTJlpZVkBE0q3/eyTEuQIqpUljl7yvs6a412knCFtSO/MPkQ... | mcq | jee-main-2014-offline | 11,623 |
PnlIt96Qke6WKAUq | physics | laws-of-motion | friction-force | <img src="data:image/png;base64,UklGRloNAABXRUJQVlA4IE4NAADQ3QCdASq4AgADP4HA3WW2Ma4nITWI8sAwCWlu/EsY+aIHZ1+/q/+t3YvskH+9zvdj/49/Afv5o1oAvv56bFW73Lf//gO//8LOskxJiTEmJMSYkxJiTEmJMSYkxIpWwZP8m6C7BNYeMLGDJ/k3QXYJihIr3ZqsfoW67BNYeMLGDJ/k3QXYJrDxhYwZP2ggkRss37IDNvMFLZbJjh4wsYMn+TdBdgmsPGFjBk/yboKz8IptL01rsRq6ZXbJISf5N0F2Caw8... | [{"identifier": "A", "content": "$$120$$ $$N$$"}, {"identifier": "B", "content": "$$150$$ $$N$$"}, {"identifier": "C", "content": "$$100$$ $$N$$"}, {"identifier": "D", "content": "$$80$$ $$N$$"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l91e0o0r/9ac128bf-b681-4232-8326-27e1c05120d4/2b6196b0-47d7-11ed-9a0e-8f7a98995d79/file-1l91e0o0s.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l91e0o0r/9ac128bf-b681-4232-8326-27e1c05120d4/2b6196b0-47d7-11ed-9a0e-8f7a98995d79/fi... | mcq | jee-main-2015-offline | 11,624 |
Xhr5sr90E677hxNpu5ZMT | physics | laws-of-motion | friction-force | A rocket is fired vertically from the earth with an acceleration of 2g, where g is the
gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass <i>m</i> is kept. The minimum coefficient of friction $$\mu $$<sub>min</sub> between the mass... | [{"identifier": "A", "content": "tan$$\\theta $$"}, {"identifier": "B", "content": "2tan$$\\theta $$"}, {"identifier": "C", "content": "3tan$$\\theta $$"}, {"identifier": "D", "content": "tan2$$\\theta $$"}] | ["A"] | null | Rocket is moving upward with acceleration 2g and gravitation acceleration is g downward direction.
<br><br>So, acceleration experienced by the point object,
<br><br>= 2g $$-$$ ($$-$$ g) = 3g
<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266922/exam_images/v8j0ks225o0p5tb0bbcb.webp" style="ma... | mcq | jee-main-2016-online-9th-april-morning-slot | 11,625 |
26hup9OWKHgKc37C | physics | laws-of-motion | friction-force | Two masses m<sub>1</sub> = 5 kg and m<sub>2</sub> = 10 kg, connected by an inextensible
string over a frictionless pulley, are moving as shown in the figure. The
coefficient of friction of horizontal surface is 0.15. The minimum
weight m that should be put on top of m<sub>2</sub> to stop the motion is :
<img src="data... | [{"identifier": "A", "content": "10.3 kg "}, {"identifier": "B", "content": "18.3 kg"}, {"identifier": "C", "content": "27.3 kg"}, {"identifier": "D", "content": "43.3 kg"}] | ["C"] | null | Moving block will stop when the friction force between m<sub>2</sub> and surface is $$ \ge $$ tension force.
<br><br>So condition for stopping the moving block,
<br><br>$$f \ge T$$
<br><br>$$ \Rightarrow \mu N \ge T$$
<br><br>$$ \Rightarrow \mu \left( {m + {m_2}} \right)g \ge {m_1}g$$
<br><br>When m is minimum then,
<b... | mcq | jee-main-2018-offline | 11,626 |
jq874BQpLYd6vzUxki8aa | physics | laws-of-motion | friction-force | A given object takes n times more time to slide down a $${45^ \circ }$$ rough inclined plane as it takes to slide down a perfectly smooth $${45^ \circ }$$ incline. The coefficient of kinetic friction between the object and the incline is : | [{"identifier": "A", "content": "$${1 \\over {2 - {n^2}}}$$ "}, {"identifier": "B", "content": "$$1 - {1 \\over {{n^2}}}$$"}, {"identifier": "C", "content": "$$\\sqrt {1 - {1 \\over {{n^2}}}} $$"}, {"identifier": "D", "content": "$$\\sqrt {{1 \\over {1 - {n^2}}}} $$ "}] | ["B"] | null | Let, t<sub>1</sub> and t<sub>2</sub> are time taken to move on the smooth and rough surface for smooth surface,
<br><br>S = $${1 \over 2}$$ g sin45<sup>o</sup> $$t_1^2$$
<br><br>$$ \Rightarrow $$$$\,\,\,\,$$ t<sub>1</sub> = $$\sqrt {{{2\sqrt 2 S} \over g}} $$
<br><br>For rough surface,
<br><br>S = $${1 \over 2}$$ g (... | mcq | jee-main-2018-online-15th-april-morning-slot | 11,627 |
BuZdpmKL3tYjIoA6oPREZ | physics | laws-of-motion | friction-force | A body of mass 2 kg slides down with an acceleration of 3 m/s<sup>2</sup> on a rough inclined plane having a slope of $${30^o}$$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s<sup>2</sup>) | [{"identifier": "A", "content": "14 N"}, {"identifier": "B", "content": "20 N"}, {"identifier": "C", "content": "6 N"}, {"identifier": "D", "content": "4 N"}] | ["B"] | null | When mass slide down then,
<br><br>Mgsin$$\theta $$ $$-$$ $$\mu $$Mg cos$$\theta $$ = Ma
<br><br>$$ \Rightarrow $$ $$\,\,\,$$ a = g(sin30<sup>o</sup> $$-$$ $$\mu $$ cos30<sup>o</sup>)
<br><br>When mass pushed upward with force F,
<br><br>F $$-$$ Mgsin$$\theta $$ $$-$$ $$\mu $$ Mgcos$$\theta $$ = Ma
<br><br>$$ \Righta... | mcq | jee-main-2018-online-15th-april-evening-slot | 11,628 |
AN5YJDwHGIRdF7qHTXemp | physics | laws-of-motion | friction-force | A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s<sup>2</sup>]
... | [{"identifier": "A", "content": "$${{\\sqrt 3 } \\over 4}$$"}, {"identifier": "B", "content": "$${1 \\over 2}$$"}, {"identifier": "C", "content": "$${{\\sqrt 3 } \\over 2}$$"}, {"identifier": "D", "content": "$${2 \\over 3}$$"}] | ["C"] | null | 2 + mg sin30 = $$\mu $$mg cos30<sup>o</sup>
<br><br>10 = mgsin30 + $$\mu $$ mg cos30<sup>o</sup>
<br><br>= 2$$\mu $$mg cos30 $$-$$ 2
<br><br>6 = $$\mu $$mg cos30
<br><br>4 = mg sin30
<br><br>$${3 \over 2} = \mu \times \sqrt 3 $$
<br><br>$$\mu $$ = $${{\sqrt 3 } \over 2}$$ | mcq | jee-main-2019-online-12th-january-evening-slot | 11,629 |
155s26BQW9eGBDl6FF3rsa0w2w9jx7fmhdh | physics | laws-of-motion | friction-force | A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an
angle of 30<sup>o</sup> with the horizontal, as shown in the figures. The coefficient of friction between the block and
floor is $$\mu $$ = 0.2. The difference between the accelerations of the blocks, in case (B) ... | [{"identifier": "A", "content": "3.2 ms<sup>\u20132</sup>"}, {"identifier": "B", "content": "0.8 ms<sup>\u20132</sup>"}, {"identifier": "C", "content": "0 ms<sup>\u20132</sup>"}, {"identifier": "D", "content": "0.4 ms<sup>\u20132</sup>"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265715/exam_images/hxusvdr20ji0bclkhhtv.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th April Evening Slot Physics - Laws of Motion Question 98 English Explanation 1">
<br><br>N =... | mcq | jee-main-2019-online-12th-april-evening-slot | 11,630 |
Ungl4S0RSE4jxQCXmZ3rsa0w2w9jwzjnaon | physics | laws-of-motion | friction-force | Two blocks A and B of masses m<sub>A </sub>= 1 kg and m<sub>B </sub>= 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide ov... | [{"identifier": "A", "content": "8 N"}, {"identifier": "B", "content": "16 N"}, {"identifier": "C", "content": "40 N"}, {"identifier": "D", "content": "12 N"}] | ["B"] | null | M<sub>A</sub> = 1 kg, M<sub>B</sub> = 3 k<br><br>
$${\mu _{AB}} = 0.2$$<br><br>
$${\mu _B} = 0.2$$<br><br>
F<sub>max</sub> = (M<sub>A</sub> + M<sub>B</sub>) × 0.2 × 10 + (M<sub>A</sub> + M<sub>B</sub>) × 0.2 × 10<br><br>
= 4 × 2 + 4 × 2 = 16
| mcq | jee-main-2019-online-10th-april-evening-slot | 11,631 |
4P9HnTpgEQcV6cPjA5Vsf | physics | laws-of-motion | friction-force | A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms<sup>$$-$$2</sup>)
<b... | [{"identifier": "A", "content": "32 N"}, {"identifier": "B", "content": "18 N"}, {"identifier": "C", "content": "23 N"}, {"identifier": "D", "content": "25 N"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267459/exam_images/v6gxd3onylf9eoggk3cb.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 9th January Morning Slot Physics - Laws of Motion Question 105 English Explanation">
<br>At equi... | mcq | jee-main-2019-online-9th-january-morning-slot | 11,632 |
OSStcN4dq5uT9ZfUU3jgy2xukfrozb4z | physics | laws-of-motion | friction-force | An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts
slipping after it is at height h from the bottom. If the coefficient of friction between the ground and
the insect is 0.75, then h is :
<br/>(g = 10 ms<sup>–2</sup>) | [{"identifier": "A", "content": "0.45 m"}, {"identifier": "B", "content": "0.60 m"}, {"identifier": "C", "content": "0.20 m"}, {"identifier": "D", "content": "0.80 m"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265144/exam_images/xzconmzuoootr6eobszf.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 6th September Morning Slot Physics - Laws of Motion Question 93 English Explanation 1">
<br><br>Fo... | mcq | jee-main-2020-online-6th-september-morning-slot | 11,633 |
R4TDSdsbcq2EURGhuN1klrir6gs | physics | laws-of-motion | friction-force | An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu$$ = 0.5, the maximum height in cm at which a stationary block will not... | [] | null | 25 | The graph for given equation is shown below<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kxfosqzt/12b521db-637e-4c81-8f3b-e3e5d4245898/b42b9280-6221-11ec-a078-91dc14c283f1/file-1kxfosqzu.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kxfosqzt/12b521db-637e-4c81-8f3b-e... | integer | jee-main-2021-online-24th-february-morning-slot | 11,634 |
i3P2ASD0HG6OP48b8X1klriunvk | physics | laws-of-motion | friction-force | The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms<sup>$$-$$2</sup>] | [] | null | 25 | Given, coefficient of static friction, $$\mu$$<sub>s</sub> = 0.2<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kxenkk3i/217fc72a-441b-408d-ae73-8e96e063b847/1e974de0-6190-11ec-b27d-5f9767b4f07e/file-1kxenkk3j.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kxenkk3i/217f... | integer | jee-main-2021-online-24th-february-morning-slot | 11,635 |
ZYF3Oo8zJ9HZpxhqoY1kltkd2s8 | physics | laws-of-motion | friction-force | As shown in the figure, a block of mass $$\sqrt 3 $$ kg is kept on a horizontal rough surface of coefficient of friction $${1 \over {3\sqrt 3 }}$$. The critical force to be applied on the vertical surface as shown at an angle 60$$^\circ$$ with horizontal such that it does not move, will be 3x. The value of x will be __... | [] | null | 3.33 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266686/exam_images/uawfmq1pyxplawp7h9se.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th February Morning Shift Physics - Laws of Motion Question 86 English Explanation">
<br>N = Mg ... | integer | jee-main-2021-online-26th-february-morning-slot | 11,636 |
5IwTAy8MTrpQTH5Vom1kmhni6x7 | physics | laws-of-motion | friction-force | A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu$$<sub>k</sub>. then, the block's acceleration 'a' is given by :<br/><br/>(g is acceleration due to gravity)<br/><br/><img src="data:image/png;base6... | [{"identifier": "A", "content": "$${F \\over m}\\cos \\theta + {\\mu _K}\\left( {g - {F \\over m}\\sin \\theta } \\right)$$"}, {"identifier": "B", "content": "$${F \\over m}\\cos \\theta - {\\mu _K}\\left( {g - {F \\over m}\\sin \\theta } \\right)$$"}, {"identifier": "C", "content": "$$-$$$${F \\over m}\\cos \\theta ... | ["B"] | null | Drawing the FBD of the block.<br><br><img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264009/exam_images/vjc987ovgmlulm3obgzr.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 16th March Morning Shift Physics - Laws of Motion Question 84... | mcq | jee-main-2021-online-16th-march-morning-shift | 11,637 |
ZW2ewmLaMKVacoPAUs1kmj49v67 | physics | laws-of-motion | friction-force | Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is $${3 \over 7}$$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ___________ N. (Round off... | [] | null | 21 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263533/exam_images/gyx6ropbq2dbxu3hri1c.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Morning Shift Physics - Laws of Motion Question 82 English Explanation">
<br>$$a = {F \... | integer | jee-main-2021-online-17th-march-morning-shift | 11,638 |
u7rWobgTog1wLqYw5U1kmkcaxiw | physics | laws-of-motion | friction-force | A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is __________ N. (Round off to the Nearest Integer) [Take g = 10 ms<sup>-2... | [] | null | 30 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264459/exam_images/i40gimu8jvymmiavecso.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Evening Shift Physics - Laws of Motion Question 80 English Explanation">
<br>$$ \becaus... | integer | jee-main-2021-online-17th-march-evening-shift | 11,639 |
qHVZi7pLJPuEIbbja31krpn7sqv | physics | laws-of-motion | friction-force | A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s<sup>2</sup>. The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____________ N. [Take g = 10 m/s<s... | [{"identifier": "A", "content": "686"}, {"identifier": "B", "content": "684"}, {"identifier": "C", "content": "714"}, {"identifier": "D", "content": "716"}] | ["A"] | null | The force equation in vertical direction is <br><br>Mg $$-$$ R = Ma<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kxpzdbsx/586fcceb-082f-4ed3-870b-09fb7d76d392/e236ce20-67ca-11ec-9473-1365722e3eb6/file-1kxpzdbsy.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kxpzdbsx/5... | mcq | jee-main-2021-online-20th-july-morning-shift | 11,641 |
1ktbvwych | physics | laws-of-motion | friction-force | The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .................. N. (take g = 10 ms<sup>-2</sup>)<br/><br/><img src="data:image/png;base64,UklGRgwMAABXRUJQVlA4IAAMAACwPwCdASpcAV8APm0ylUckIyIhJxLL4IANi... | [] | null | 15 | F = 3a (For system) ............ (i)<br><br> <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263915/exam_images/owgqo349kyyjw3wiuv4y.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 26th August Evening Shift Physics - Laws of Motion Qu... | integer | jee-main-2021-online-26th-august-evening-shift | 11,643 |
1ktmuipux | physics | laws-of-motion | friction-force | When a body slides down from rest along a smooth inclined plane making an angle of 30$$^\circ$$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha$$T, where $$\alpha$$ is a constant g... | [] | null | 3 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kwosodfn/ed9bd245-b1ab-439f-891c-65071a8882e6/b5711530-5357-11ec-b443-85f16d0c41b6/file-1kwosodfo.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kwosodfn/ed9bd245-b1ab-439f-891c-65071a8882e6/b5711530-5357-11ec-b443-85f16d0c41b6/fi... | integer | jee-main-2021-online-1st-september-evening-shift | 11,644 |
1l54vaigo | physics | laws-of-motion | friction-force | <p>A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.</p>
<p>The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is. (Given g = 10 ms<sup>$$-$$2</sup>.)</p... | [{"identifier": "A", "content": "1 ms<sup>$$-$$2</sup>"}, {"identifier": "B", "content": "1/5 ms<sup>$$-$$2</sup>"}, {"identifier": "C", "content": "4/5 ms<sup>$$-$$2</sup>"}, {"identifier": "D", "content": "8/11 ms<sup>$$-$$2</sup>"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5gh4osf/8fa79ab2-c295-4528-98d8-9100492cb6a4/3ad33800-00f2-11ed-ba34-71a54c393c2b/file-1l5gh4osg.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5gh4osf/8fa79ab2-c295-4528-98d8-9100492cb6a4/3ad33800-00f2-11ed-ba34-71a54c393c2b... | mcq | jee-main-2022-online-29th-june-evening-shift | 11,645 |
1l57pohad | physics | laws-of-motion | friction-force | <p>A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be :</p>
<p> <img src="data:image/png;ba... | [{"identifier": "A", "content": "9.8 N"}, {"identifier": "B", "content": "39.2 N"}, {"identifier": "C", "content": "49 N"}, {"identifier": "D", "content": "78.4 N"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l5jqh85b/7654cfc9-efe9-449a-b94e-14f444f01390/239930f0-02bd-11ed-95db-c3fa9a0f41ba/file-1l5jqh85c.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l5jqh85b/7654cfc9-efe9-449a-b94e-14f444f01390/239930f0-02bd-11ed-95db-c3fa9a0f41ba... | mcq | jee-main-2022-online-27th-june-morning-shift | 11,646 |
1l5c2wdv0 | physics | laws-of-motion | friction-force | <p>A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms<sup>$$-$$1</sup>. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is :</p>
<p>[use g = 9.8 ms<sup>$$-$$2</sup>]</p> | [{"identifier": "A", "content": "4.9 m"}, {"identifier": "B", "content": "9.8 m"}, {"identifier": "C", "content": "12.5 m"}, {"identifier": "D", "content": "19.6 m"}] | ["B"] | null | <p>$$S = {{{u^2}} \over {2a}} = {{{u^2}} \over {2(\mu g)}}$$</p>
<p>$$ = {{{{(9.8)}^2}} \over {2 \times 0.5 \times (9.8)}}$$</p>
<p>$$ = {{9.8} \over 1}$$</p>
<p>$$ = 9.8$$ m</p> | mcq | jee-main-2022-online-24th-june-morning-shift | 11,647 |
1l5w247bn | physics | laws-of-motion | friction-force | <p>A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). The maximum value of F applied, so that the block does not move upward, will ... | [{"identifier": "A", "content": "10 N"}, {"identifier": "B", "content": "20 N"}, {"identifier": "C", "content": "25 N"}, {"identifier": "D", "content": "45 N"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6dmnj3o/1ca80253-c1f5-4ad4-b963-304a23a853cc/b1e19340-132d-11ed-941a-4dd6502f33e3/file-1l6dmnj3p.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6dmnj3o/1ca80253-c1f5-4ad4-b963-304a23a853cc/b1e19340-132d-11ed-941a-4dd6502f33e3... | mcq | jee-main-2022-online-30th-june-morning-shift | 11,648 |
1l6jh0kik | physics | laws-of-motion | friction-force | <p>A bag is gently dropped on a conveyor belt moving at a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The coefficient of friction between the conveyor belt and bag is $$0.4$$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion, is : [T... | [{"identifier": "A", "content": "2 m"}, {"identifier": "B", "content": "0.5 m"}, {"identifier": "C", "content": "3.2 m"}, {"identifier": "D", "content": "0.8 ms"}] | ["B"] | null | Speed of conveyor belt, $v=2 \mathrm{~m} / \mathrm{s}$
<br/><br/>Coefficient of friction between the conveyor belt and bag, $\mu=0.4$
<br/><br/>Acceleration of bag due to slipping motion,
<br/><br/>$$
a=\mu g=0.4 \times 10=4 \mathrm{~m} / \mathrm{s}^2 \quad\left(\because g=10 \mathrm{~m} / \mathrm{s}^2\right)
$$
<br/><... | mcq | jee-main-2022-online-27th-july-morning-shift | 11,649 |
1ldnx4lar | physics | laws-of-motion | friction-force | <p>As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30^\circ$$, with horizontal. For $$\mu_s=0.25$$, the block will just start to move for the value of F : [Given $$g=10~\mathrm{ms}^{-2}$$]</p>
<p><img src="data:image/png;base64,UklGRuYNAABXRUJQVlA4I... | [{"identifier": "A", "content": "25.2 N"}, {"identifier": "B", "content": "35.7 N"}, {"identifier": "C", "content": "20 N"}, {"identifier": "D", "content": "33.3 N"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1le2xzpc4/1af3a8a9-1c75-49d7-88ba-579c2e134693/24b71c40-abaf-11ed-a6ae-f1aa1b068e73/file-1le2xzpc6.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1le2xzpc4/1af3a8a9-1c75-49d7-88ba-579c2e134693/24b71c40-abaf-11ed-a6ae-f1aa1b068e73/fi... | mcq | jee-main-2023-online-1st-february-evening-shift | 11,650 |
ldo6u481 | physics | laws-of-motion | friction-force | A body of mass $10 \mathrm{~kg}$ is moving with an initial speed of $20 \mathrm{~m} / \mathrm{s}$. The body stops after $5 \mathrm{~s}$ due to friction between body and the floor. The value of the coefficient of friction is: <br/><br/>(Take acceleration due to gravity $g=10 \mathrm{~ms}^{-2}$ ) | [{"identifier": "A", "content": "0.3"}, {"identifier": "B", "content": "0.2"}, {"identifier": "C", "content": "0.5"}, {"identifier": "D", "content": "0.4"}] | ["D"] | null | $a=-\mu g$
<br/><br/>$$
\begin{aligned}
& \because v=u+a t \\\\
& 0=20+(-\mu \times 10) \times 5 \\\\
& 50 \mu=20 \\\\
& \mu=\frac{2}{5}=0.4
\end{aligned}
$$ | mcq | jee-main-2023-online-31st-january-evening-shift | 11,651 |
1ldsoychw | physics | laws-of-motion | friction-force | <p>A block of mass $m$ slides down the plane inclined at angle $$30^{\circ}$$ with an acceleration $$\frac{g}{4}$$. The value of coefficient of kinetic friction will be:</p> | [{"identifier": "A", "content": "$$\\frac{2 \\sqrt{3}-1}{2}$$"}, {"identifier": "B", "content": "$$\\frac{\\sqrt{3}}{2}$$"}, {"identifier": "C", "content": "$$\\frac{1}{2 \\sqrt{3}}$$"}, {"identifier": "D", "content": "$$\\frac{2 \\sqrt{3}+1}{2}$$"}] | ["C"] | null | $\mathrm{Mg} \sin 30^{\circ}-\mu \mathrm{mg} \cos 30^{\circ}=\mathrm{ma}$<br><br>
$$
\frac{g}{2}-\frac{\sqrt{3}}{2} \cdot \mu g=\frac{g}{4}
$$<br><br>
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lei28qih/bb511db9-cd31-42a2-a1d3-34c5b40efd18/8629eb80-b3ff-11ed-8ae6-addab6c4d98a/file-1lei28qii.png?fo... | mcq | jee-main-2023-online-29th-january-morning-shift | 11,654 |
1ldtxt5w5 | physics | laws-of-motion | friction-force | <p>Consider a block kept on an inclined plane (incline at 45$$^\circ$$) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane($$\mu$$) is equal to :</p>
<p><img src... | [{"identifier": "A", "content": "0.60"}, {"identifier": "B", "content": "0.33"}, {"identifier": "C", "content": "0.25"}, {"identifier": "D", "content": "0.50"}] | ["B"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1ledld6l4/ad6f6b7b-570b-431c-b903-d9561dd76b67/64062180-b18a-11ed-a682-13f364283dca/file-1ledld6l5.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1ledld6l4/ad6f6b7b-570b-431c-b903-d9561dd76b67/64062180-b18a-11ed-a682-13f364283dca... | mcq | jee-main-2023-online-25th-january-evening-shift | 11,655 |
jaoe38c1lscp0asi | physics | laws-of-motion | friction-force | <p>Given below are two statements :</p>
<p>Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.</p>
<p>Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials.</p>
<p>In the light of the above st... | [{"identifier": "A", "content": "Statement I is incorrect but Statement II is correct\n"}, {"identifier": "B", "content": "Both Statement I and Statement II are correct\n"}, {"identifier": "C", "content": "Both Statement I and Statement II are incorrect\n"}, {"identifier": "D", "content": "Statement I is correct but St... | ["A"] | null | <p>Let's analyze both statements:</p>
<p><strong>Statement (I): The limiting force of static friction depends on the area of contact and independent of materials.</strong>
<br/><br/>This statement is incorrect. The limiting force of static friction does not depend on the area of contact but is dependent on the mate... | mcq | jee-main-2024-online-27th-january-evening-shift | 11,656 |
lv3ve86t | physics | laws-of-motion | friction-force | <p>A given object takes $$\mathrm{n}$$ times the time to slide down $$45^{\circ}$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45^{\circ}$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :</p> | [{"identifier": "A", "content": "$$1-\\frac{1}{\\mathrm{n}^2}$$\n"}, {"identifier": "B", "content": "$$\\sqrt{1-\\frac{1}{\\mathrm{n}^2}}$$\n"}, {"identifier": "C", "content": "$$1-n^2$$\n"}, {"identifier": "D", "content": "$$\\sqrt{1-n^2}$$"}] | ["A"] | null | <p>To determine the coefficient of kinetic friction, let's analyze the time taken by the object to slide down each plane and use the equations of motion for both scenarios. </p>
<p>First, consider the perfectly smooth $$45^{\circ}$$ inclined plane (no friction). The acceleration of the object on this plane can be calc... | mcq | jee-main-2024-online-8th-april-evening-shift | 11,658 |
lv9s20wg | physics | laws-of-motion | friction-force | <p>A heavy box of mass $$50 \mathrm{~kg}$$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :</p> | [{"identifier": "A", "content": "1470 N"}, {"identifier": "B", "content": "147 N"}, {"identifier": "C", "content": "1.47 N"}, {"identifier": "D", "content": "14.7 N"}] | ["B"] | null | <p>To find the force of kinetic friction acting on the box, we can use the formula for kinetic friction, which is given by:</p>
<p>$F_{\text{friction}} = \mu_{k} \cdot N$</p>
<p>where:</p>
<ul>
<li>$F_{\text{friction}}$ is the force of friction,</li>
<li>$\mu_{k}$ is the coefficient of kinetic friction,</li>
<li>... | mcq | jee-main-2024-online-5th-april-evening-shift | 11,659 |
PVj9lnQsnNNTeGT1 | physics | laws-of-motion | motion-of-connected-bodies | Three identical blocks of masses $$m=2$$ $$kg$$ are drawn by a force $$F=10.2$$ $$N$$ with an acceleration of $$0.6$$ $$m{s^{ - 2}}$$ on a frictionless surface, then what is the tension (in $$N$$) in the string between the blocks $$B$$ and $$C$$?
<img src="data:image/png;base64,UklGRjwbAABXRUJQVlA4IDAbAACwbACdASpzAq0A... | [{"identifier": "A", "content": "$$9.2$$ "}, {"identifier": "B", "content": "$$3.4$$ "}, {"identifier": "C", "content": "$$4$$ "}, {"identifier": "D", "content": "$$7.8$$ "}] | ["D"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/x2FmAI5ZkWfYZuLJz/dt1HRyLTG8cAVDMP7n5uHcRUEY5SQ/G8BWyQfjCrKGMztjP2HcHF/image.svg" loading="lazy" alt="AIEEE 2002 Physics - Laws of Motion Question 130 English Explanation">
Assume tension between block A and B is T<sub>1</sub> and block B and C is T<sub>2... | mcq | aieee-2002 | 11,660 |
woTFOhnXmDwnCvCc | physics | laws-of-motion | motion-of-connected-bodies | One end of a mass-less rope, which passes over a mass-less and friction-less pulley $$P$$ is tied to a hook $$C$$ while the other end is free. Maximum tension that the rope can bear is $$360$$ $$N.$$ With what value of maximum safe acceleration (in $$m{s^{ - 2}}$$) can a man of $$60$$ $$kg$$ climb on the rope?
<img sr... | [{"identifier": "A", "content": "$$16$$ "}, {"identifier": "B", "content": "$$6$$"}, {"identifier": "C", "content": "$$4$$ "}, {"identifier": "D", "content": "$$8$$ "}] | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/t6pfr29EvOJPsfiLf/VImuar68D1TfQZfJVDhHyPPKRLyss/paNlvp02BtwqyNUJDIYB8A/image.svg" loading="lazy" alt="AIEEE 2002 Physics - Laws of Motion Question 117 English Explanation">
Assuming acceleration $$a$$ of the man is downwards.
So the equation will be
<br><... | mcq | aieee-2002 | 11,661 |
aWWfFnaJRzIC4zNN | physics | laws-of-motion | motion-of-connected-bodies | A light string passing over a smooth light pulley connects two blocks of masses $${m_1}$$ and $${m_2}$$ (vertically). If the acceleration of the system is $$g/8$$, then the ratio of the masses is | [{"identifier": "A", "content": "$$8:1$$ "}, {"identifier": "B", "content": "$$9:7$$ "}, {"identifier": "C", "content": "$$4:3$$ "}, {"identifier": "D", "content": "$$5:3$$ "}] | ["B"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/9MvQ7O4PYGVeql15b/kJzIkBlaShxXoe1mPdUtuEJ8r5lnM/sRxIB6wFPnsk3JiEmdovWO/image.svg" loading="lazy" alt="AIEEE 2002 Physics - Laws of Motion Question 131 English Explanation">
<br>Assume that, mass m<sub>1</sub> is greater than mass m<sub>2</sub>, so the he... | mcq | aieee-2002 | 11,662 |
sVFEgsQBtOfzoKRX | physics | laws-of-motion | motion-of-connected-bodies | A block of mass $$M$$ is pulled along a horizontal frictionless surface by a rope of mass $$m.$$ If a force $$P$$ is applied at the free end of the rope, the force exerted by the rope on the block is | [{"identifier": "A", "content": "$${{Pm} \\over {M + m}}$$ "}, {"identifier": "B", "content": "$${{Pm} \\over {M - m}}$$ "}, {"identifier": "C", "content": "$$P$$ "}, {"identifier": "D", "content": "$${{PM} \\over {M + m}}$$ "}] | ["D"] | null | Taking the rope and the block as a system
<img class="question-image" src="https://imagex.cdn.examgoal.net/QzeN6sAzULjryTY7e/exJ1b4zrxQr0QQvzuRaLyQyb0nO0p/2xcKOfRrd4yKHRRPrmU1DW/image.svg" loading="lazy" alt="AIEEE 2003 Physics - Laws of Motion Question 127 English Explanation">
<br>Acceleration of block($$a$$) = $${{... | mcq | aieee-2003 | 11,663 |
O3wqPzUSTxMpFWLL | physics | laws-of-motion | motion-of-connected-bodies | Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $$\left( {g = 9.8m/{s^2}} \right)$$
<img src="data:image/png;base64,UklGRlAUAABXRUJQVlA4IEQUAABQtACdASoAAw4CP4HA1mY2MawnIb3YisAwCWlu/HyZcetQ3v7n/... | [{"identifier": "A", "content": "$$5\\,\\,m/{s^2}$$ "}, {"identifier": "B", "content": "$$9.8\\,\\,m/{s^2}$$"}, {"identifier": "C", "content": "$$0.2\\,\\,m/{s^2}$$"}, {"identifier": "D", "content": "$$4.8\\,\\,m/{s^2}$$"}] | ["C"] | null | <img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265159/exam_images/cf3wfn0xuzl0vpzbbozb.webp" loading="lazy" alt="AIEEE 2004 Physics - Laws of Motion Question 124 English Explanation">
<br><b>For m<sub>1</sub> mass :</b>
<br><br>m<sub>1</sub>g - T = m<sub>1</sub>a .........(1)... | mcq | aieee-2004 | 11,664 |
1ktfj9jk8 | physics | laws-of-motion | motion-of-connected-bodies | The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s<sup>2</sup>)<br/><br/><img src="data:image/png;base64,UklGRvAdAABXRUJQVlA4IOQdAACQjACdASogAVoBPm0ylUgkIqIhJxJqoIANiWlu4XU... | [{"identifier": "A", "content": "0.34 s"}, {"identifier": "B", "content": "0.2 s"}, {"identifier": "C", "content": "0.25 s"}, {"identifier": "D", "content": "0.4 s"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266170/exam_images/wzeti7svtigswrm3hdsz.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 27th August Evening Shift Physics - Laws of Motion Question 72 English Explanation"><br>(m<sub>1</... | mcq | jee-main-2021-online-27th-august-evening-shift | 11,665 |
1l56ac5he | physics | laws-of-motion | motion-of-connected-bodies | <p>A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $${x \over 5}$$ Mg for x = ______________. Neglect mass of the string ... | [] | null | 6 | <p>$$a = {{Mg} \over {4M + M}} = {g \over 5}$$ (in upward direction)</p>
<p>$$T = M\left( {g + {g \over 5}} \right) = {{6Mg} \over 5}$$</p>
<p>$$ \Rightarrow x = 6$$</p> | integer | jee-main-2022-online-28th-june-morning-shift | 11,666 |
1l58hctw3 | physics | laws-of-motion | motion-of-connected-bodies | <p>In the arrangement shown in figure a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub> and a<sub>4</sub> are the accelerations of masses m<sub>1</sub>, m<sub>2</sub>, m<sub>3</sub> and m<sub>4</sub> respectively. Which of the following relation is true for this arrangement?</p>
<p><img src="data:image/png;base64,UklGRiAJAAB... | [{"identifier": "A", "content": "4a<sub>1</sub> + 2a<sub>2</sub> + a<sub>3</sub> + a<sub>4</sub> = 0"}, {"identifier": "B", "content": "a<sub>1</sub> + 4a<sub>2</sub> + 3a<sub>3</sub> + a<sub>4</sub> = 0"}, {"identifier": "C", "content": "a<sub>1</sub> + 4a<sub>2</sub> + 3a<sub>3</sub> + 2a<sub>4</sub> = 0"}, {"identif... | ["A"] | null | <p>From virtual work done method,</p>
<p>4T $$\times$$ a<sub>1</sub> + 2T $$\times$$ a<sub>2</sub> + T $$\times$$ a<sub>3</sub> + T $$\times$$ a<sub>4</sub> = 0</p>
<p>$$\Rightarrow$$ 4a<sub>1</sub> + 2a<sub>2</sub> + a<sub>3</sub> + a<sub>4</sub> = 0</p> | mcq | jee-main-2022-online-26th-june-evening-shift | 11,667 |
1l6gjuev8 | physics | laws-of-motion | motion-of-connected-bodies | <p>Three masses $$M=100 \mathrm{~kg}, \mathrm{~m}_{1}=10 \mathrm{~kg}$$ and $$\mathrm{m}_{2}=20 \mathrm{~kg}$$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $$\mathrm{F}$$ is applied o... | [{"identifier": "A", "content": "3360 N"}, {"identifier": "B", "content": "3380 N"}, {"identifier": "C", "content": "3120 N"}, {"identifier": "D", "content": "3240 N"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m0knqwn0/cf816dc2-8bde-4355-9f37-69d589e0be11/f2cf1de0-68f9-11ef-81b7-2985a08ef4a0/file-jaoe38c1m0knqwn2.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/jaoe38c1m0knqwn0/cf816dc2-8bde-4355-9f37-69d589e0be11/f2cf1de0-68f9-1... | mcq | jee-main-2022-online-26th-july-morning-shift | 11,669 |
1l6i1nvbu | physics | laws-of-motion | motion-of-connected-bodies | <p>Two masses $$M_{1}$$ and $$M_{2}$$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $$M_{2}$$ is twice that of $$M_{1}$$, the acceleration of the system is $$a_{1}$$. When the mass $$M_{2}$$ is thrice that of $$M_{1}$$, the acceleration of the sys... | [{"identifier": "A", "content": "$$\\frac{1}{3}$$"}, {"identifier": "B", "content": "$$\\frac{2}{3}$$"}, {"identifier": "C", "content": "$$\\frac{3}{2}$$"}, {"identifier": "D", "content": "$$\\frac{1}{2}$$"}] | ["B"] | null | <p>$${a_1} = {{{M_2} - {M_1}} \over {{M_2} + {M_1}}} \times g = {{2{M_1} - {M_1}} \over {3{M_1}}} \times g$$</p>
<p>$$ = {g \over 3}$$</p>
<p>And, $${a_2} = {{3{M_1} - {M_1}} \over {4{M_1}}} \times g = {g \over 2}$$</p>
<p>$$\therefore$$ $${{{a_1}} \over {{a_2}}} = {{g/3} \over {g/2}} = {2 \over 3}$$</p> | mcq | jee-main-2022-online-26th-july-evening-shift | 11,670 |
1l6nq48hi | physics | laws-of-motion | motion-of-connected-bodies | <p>A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length '$$\mathrm{L}-l$$' is hanging on the other side of the pully. At a certain point of time, when $$l=\frac{L}{x}$$, the acc... | [{"identifier": "A", "content": "6"}, {"identifier": "B", "content": "2"}, {"identifier": "C", "content": "1.5"}, {"identifier": "D", "content": "4"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6zshim0/4c44e700-acf1-4f8f-ac83-2830ec51dfdb/bfb5b690-1f5d-11ed-a57c-4f5194e3f05f/file-1l6zshim1.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6zshim0/4c44e700-acf1-4f8f-ac83-2830ec51dfdb/bfb5b690-1f5d-11ed-a57c-4f5194e3f05f... | mcq | jee-main-2022-online-28th-july-evening-shift | 11,671 |
1l6rhex6q | physics | laws-of-motion | motion-of-connected-bodies | <p>Two bodies of masses $$m_{1}=5 \mathrm{~kg}$$ and $$m_{2}=3 \mathrm{~kg}$$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $$\mathrm{m}_{1}$$ will be : [Take $$\left.... | [{"identifier": "A", "content": "30 N"}, {"identifier": "B", "content": "40 N"}, {"identifier": "C", "content": "50 N"}, {"identifier": "D", "content": "60 N"}] | ["B"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lbz80yr2/da68da77-baff-44bf-98b3-d119f2ff852f/d1bb99d0-820a-11ed-85f3-c356c5c15235/file-1lbz80yr3.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lbz80yr2/da68da77-baff-44bf-98b3-d119f2ff852f/d1bb99d0-820a-11ed-85f3-c356c5c15235/fi... | mcq | jee-main-2022-online-29th-july-evening-shift | 11,672 |
lsbkj8ah | physics | laws-of-motion | motion-of-connected-bodies | Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in $\mathrm{ms}^{-2}$ is :<br/><br/>
(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :<br/... | [{"identifier": "A", "content": "1.2"}, {"identifier": "B", "content": "4"}, {"identifier": "C", "content": "3"}, {"identifier": "D", "content": "2"}] | ["D"] | null | $\begin{aligned} & 60-f_k=(20+6) a \\\\ & 60-200 \times 0.04=26 a \Rightarrow a=2 \mathrm{~m} / \mathrm{s}^2\end{aligned}$ | mcq | jee-main-2024-online-1st-february-morning-shift | 11,674 |
jaoe38c1lsd5y0lv | physics | laws-of-motion | motion-of-connected-bodies | <p>A light string passing over a smooth light fixed pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$g / 8$$, then the ratio of masses is:</p>
<p><img src="data:image/png;base64,UklGRgQLAABXRUJQVlA4IPgKAAAQvgCdASoZAgADP4G+2GY2L6ynIVGJIsAwCWlu/CiVnZ+x/r18tDOzr9/ZzdX1lTvBcS... | [{"identifier": "A", "content": "$$\\frac{8}{1}$$"}, {"identifier": "B", "content": "$$\\frac{9}{7}$$"}, {"identifier": "C", "content": "$$\\frac{5}{3}$$"}, {"identifier": "D", "content": "$$\\frac{4}{3}$$"}] | ["B"] | null | <p>$$\begin{aligned}
& a=\frac{\left(m_1-m_2\right) g}{\left(m_1+m_2\right)}=\frac{g}{8} \\
& 8 m_1-8 m_2=m_1+m_2 \\
& 7 m_1=9 m_2 \\
& \frac{m_1}{m_2}=\frac{9}{7}
\end{aligned}$$</p> | mcq | jee-main-2024-online-31st-january-evening-shift | 11,675 |
jaoe38c1lse65jrw | physics | laws-of-motion | motion-of-connected-bodies | <p>In the given arrangement of a doubly inclined plane two blocks of masses $$M$$ and $$m$$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $$m$$, for which $$M=10 \mathrm{~kg}... | [{"identifier": "A", "content": "4.5 kg"}, {"identifier": "B", "content": "6.5 kg"}, {"identifier": "C", "content": "9 kg"}, {"identifier": "D", "content": "2.25 kg"}] | ["A"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsluiior/2d82d9b6-a66e-4927-91f0-62b7dc49fb77/77146eb0-cb3f-11ee-ad47-a16d1086e690/file-6y3zli1lsluiios.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsluiior/2d82d9b6-a66e-4927-91f0-62b7dc49fb77/77146eb0-cb3f-11ee... | mcq | jee-main-2024-online-31st-january-morning-shift | 11,676 |
1lsgwz89q | physics | laws-of-motion | motion-of-connected-bodies | <p>All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $$2 \mathrm{~kg}$$ is :</p>
<p><img src="data:image/png;base64,UklGRmYQAABXRUJQVlA4IFoQAAAw+QCdASoAAxsCP4HA2GU2MCynIdK5gsAwCWlu+F6oMD9ZNlu56V/4vrEupV/WJf5Tm+e6Ht31f/vQQsVf/QVkwv... | [{"identifier": "A", "content": "$$\\mathrm{\\frac{g}{2}}$$"}, {"identifier": "B", "content": "$$\\mathrm{\\frac{g}{4}}$$"}, {"identifier": "C", "content": "$$\\mathrm{g}$$"}, {"identifier": "D", "content": "$$\\mathrm{\\frac{g}{3}}$$"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsqm3q74/65d5bd2b-cae9-4e47-af5e-ca877e75a4d8/7df53600-cdde-11ee-a0d3-7b75c4537559/file-6y3zli1lsqm3q75.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsqm3q74/65d5bd2b-cae9-4e47-af5e-ca877e75a4d8/7df53600-cdde-11ee... | mcq | jee-main-2024-online-30th-january-morning-shift | 11,678 |
lv7v4rip | physics | laws-of-motion | motion-of-connected-bodies | <p>Three blocks $$\mathrm{M_1, M_2, M_3}$$ having masses $$4 \mathrm{~kg}, 6 \mathrm{~kg}$$ and $$10 \mathrm{~kg}$$ respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope $$\mathrm{1, T_1}$$ when they are moving upward with acceleration of $$2 \mathrm{~ms}^{-2}$$ ... | [] | null | 240 | <p>$$\begin{aligned}
& T_1-(4+6+10) g=(4+6+10)(2) \\
& \Rightarrow T_1=20(10+2) \\
& \quad=240 \mathrm{~N}
\end{aligned}$$</p> | integer | jee-main-2024-online-5th-april-morning-shift | 11,680 |
lvc5836l | physics | laws-of-motion | motion-of-connected-bodies | <p>A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $$\left.m_2>m_1\right)$$. If the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, then the ratio of the masses $$\frac{m_1}{m_2}$$ is:</p> | [{"identifier": "A", "content": "$$\\frac{1+\\sqrt{5}}{\\sqrt{5}-1}$$\n"}, {"identifier": "B", "content": "$$\\frac{\\sqrt{3}+1}{\\sqrt{2}-1}$$\n"}, {"identifier": "C", "content": "$$\\frac{\\sqrt{2}-1}{\\sqrt{2}+1}$$\n"}, {"identifier": "D", "content": "$$\\frac{1+\\sqrt{5}}{\\sqrt{2}-1}$$"}] | ["C"] | null | <p>Given that the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, let's analyze the forces acting on both masses to find the ratio $$\frac{m_1}{m_2}$$.</p>
<p>The tension force in the string is equal for both masses since the pulley and string are light and smooth. Assuming the pulley only changes the direction ... | mcq | jee-main-2024-online-6th-april-morning-shift | 11,681 |
PXvqrrEs34ZSmIjz | physics | laws-of-motion | motion-on-an-inclined-plane | A block is kept on a frictionless inclined surface with angle of inclination $$'\,\alpha \,'.$$ The incline is given an acceleration $$a$$ to keep the block stationary. Then $$a$$ is equal to
<img src="data:image/png;base64,UklGRtgJAABXRUJQVlA4IMwJAAAwUwCdASrmAT0BPm02mEkkIqKhIZco0IANiWlu4XVRG/OZ8Zf4Xtp/y3hz5GvZvtZld3z... | [{"identifier": "A", "content": "$$g$$ $$cosec$$ $$\\alpha $$ "}, {"identifier": "B", "content": "$$g/tan$$ $$\\alpha $$"}, {"identifier": "C", "content": "$$g$$ $$tan$$ $$\\alpha $$"}, {"identifier": "D", "content": "$$g$$ "}] | ["C"] | null | Acceleration of the block is to the right. Pseudo force acting on the block to the left.
<br><br><img class="question-image" src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265462/exam_images/w32zbigtlgc0o9hxxek3.webp" loading="lazy" alt="AIEEE 2005 Physics - Laws of Motion Question 114 English Explanation"... | mcq | aieee-2005 | 11,682 |
nsNOXFb1o8rlP9u3 | physics | laws-of-motion | motion-on-an-inclined-plane | Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown in the figure. Two blocks $$A$$ and $$B$$ are placed on the two planes. What is the relative vertical acceleration of $$A$$ with respect to $$B$$ ?
<img src="data:image/png;base64,UklGRpIKAABXRUJQVl... | [{"identifier": "A", "content": "$$4.9m{s^{ - 2}}$$ in horizontal direction"}, {"identifier": "B", "content": "$$9.8m{s^{ - 2}}$$ in vertical direction "}, {"identifier": "C", "content": "Zero "}, {"identifier": "D", "content": "$$4.9m{s^{ - 2}}$$ in vertical direction "}] | ["D"] | null | Along inclined plane the equation of motion of the body
<br><br>$$mg\,\sin \,\theta = ma$$ $$\,\,\,\,\,\,\,\,$$ $$\therefore$$ $$a = g\,\sin \,\theta $$
<br><br>where $$a$$ is along the inclined plane.
<br><br>$$\therefore$$ vertical component of acceleration is $$\left( {g\sin \theta } \right)\sin \theta $$ = $$g\,{... | mcq | aieee-2010 | 11,683 |
1kth6l7u4 | physics | laws-of-motion | motion-on-an-inclined-plane | A car is moving on a plane inclined at 30$$^\circ$$ to the horizontal with an acceleration of 10 ms<sup>$$-$$2</sup> parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ______________. (Take g = 10 ms<sup>$$-$$2</sup>) | [] | null | 30 | <p>Given,</p>
<p>Angle of inclination, $$\theta$$ = 30$$^\circ$$</p>
<p>Acceleration, a = 10 ms<sup>$$-$$2</sup></p>
<p>Acceleration due to gravity, g = 10 ms<sup>$$-$$2</sup></p>
<p>According to the question the car and bob is as shown below,</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l14p... | integer | jee-main-2021-online-31st-august-morning-shift | 11,684 |
1ktmnoiti | physics | laws-of-motion | motion-on-an-inclined-plane | A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.<br/><br/>
<img src="data:image/png;base64,UklGRhgIAABXRUJQVlA4IAwI... | [{"identifier": "A", "content": "$${4 \\over 3}g$$"}, {"identifier": "B", "content": "$${6 \\over 5}g$$"}, {"identifier": "C", "content": "$${3 \\over 5}g$$"}, {"identifier": "D", "content": "$${2 \\over 3}g$$"}] | ["D"] | null | Let acceleration of wedge is a<sub>w</sub> and acceleration of block w.r.t. wedge is a<sub>b</sub>
<br><br>For the wedge w.r.t. ground
<br><br>
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kwlelbby/ea3c8b3c-09de-4b53-8659-9d4e2eb37e29/46a23be0-517a-11ec-b272-9de10c41dd18/file-1kwlelbbz.png?format=pn... | mcq | jee-main-2021-online-1st-september-evening-shift | 11,685 |
1ktmozwvm | physics | laws-of-motion | motion-on-an-inclined-plane | An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile.<br/><br/><img src="data:image/png;base64,UklGRsgLAABXRUJQVlA4ILwLAABwyQCdASoAA7sBP4HA2mS2Ma0nIpM5esAwCWlu+E5oMB05Nlu52g9aF/dhHuse1fF4Q6PZ+Zv+1ef+1ssdFw6tf... | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1kwor71pp/4f7e5512-d7b3-4998-8028-45ce3d3dcbc7/ea80d1d0-5351-11ec-9cbb-695a838b20fb/file-1kwor71pq.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1kwor71pp/4f7e5512-d7b3-4998-8028-45ce3d3dcbc7/ea8... | ["C"] | null | During upward motion<br><br>F = 2N = (+ve) constant
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kx9xobjv/bf54d8c6-388f-4241-8cef-58d6bd7e374f/b7457bc0-5ef7-11ec-85b8-4b78fdd0cc43/file-1kx9xobjw.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kx9xobjv/bf54d8c6-388f-4... | mcq | jee-main-2021-online-1st-september-evening-shift | 11,686 |
1l6kmgbm9 | physics | laws-of-motion | motion-on-an-inclined-plane | <p>A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $$\theta$$. The magnitude of the contact force will be :</p> | [{"identifier": "A", "content": "Mg"}, {"identifier": "B", "content": "$$\\mathrm{Mg} \\cos \\theta$$"}, {"identifier": "C", "content": "$$\\sqrt{\\mathrm{Mg} \\sin \\theta+\\mathrm{Mg} \\cos \\theta}$$"}, {"identifier": "D", "content": "$$\\operatorname{Mg} \\sin \\theta \\sqrt{1+\\mu}$$"}] | ["A"] | null | <p>As the body is moving with constant velocity so forces acting on the body must be balanced.</p>
<p>$$\Rightarrow$$ Contact force from incline should balance weight of the body.</p>
<p>$$\Rightarrow$$ | F<sub>contact</sub> | = Mg</p> | mcq | jee-main-2022-online-27th-july-evening-shift | 11,687 |
1l6kmjisk | physics | laws-of-motion | motion-on-an-inclined-plane | <p>A block 'A' takes 2 s to slide down a frictionless incline of 30$$^\circ$$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45$$^\circ$$, the time taken by the block, to slide down the incline, will be approximately :</p> | [{"identifier": "A", "content": "2.66 s"}, {"identifier": "B", "content": "0.83 s"}, {"identifier": "C", "content": "1.68 s"}, {"identifier": "D", "content": "0.70 s"}] | ["C"] | null | <p>$${\theta _1} = 30^\circ ,\,{\theta _2} = 45^\circ $$</p>
<p>$${a_1} = g\sin {\theta _1} = 5$$ m/s<sup>2</sup>, $${a_2} = g\sin {\theta _2} = 5\sqrt 2 $$ m/s<sup>2</sup></p>
<p>$${{{t_1}} \over {{t_2}}} = {{\sqrt {{{2l} \over {{a_1}}}} } \over {\sqrt {{{2l} \over {{a_2}}}} }} = \sqrt {{{{a_2}} \over {{a_1}}}} $$</p>... | mcq | jee-main-2022-online-27th-july-evening-shift | 11,688 |
1l6koqgw0 | physics | laws-of-motion | motion-on-an-inclined-plane | <p>Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C... | [] | null | 2 | <p>$$AB = 10\sqrt 2 $$ m</p>
<p>$${v_A} = \sqrt {2 \times 10 \times 10} = 10\sqrt 2 $$ m/s</p>
<p>$${v_C} = 10\sqrt 2 $$ m/s</p>
<p>$${a_{BC}} = g\sin (30^\circ ) = 5$$ m/s<sup>2</sup></p>
<p>$${t_{BC}} = 2\sqrt 2 \,s\,\left( {{{{v_c}} \over {{a_{BC}}}}} \right)$$</p>
<p>$${t_{AB}} = {{{v_A}} \over {5\sqrt 2 }} = 2\,s... | integer | jee-main-2022-online-27th-july-evening-shift | 11,689 |
jaoe38c1lsd5rads | physics | laws-of-motion | motion-on-an-inclined-plane | <p><img src="data:image/png;base64,UklGRgQOAABXRUJQVlA4IPgNAACQBQGdASrfAgADP4HA3GW2MK2nIbHoysAwCWlu/HyYhVsnZ1+/sV+KPvK4dPSGIl+h8/XaTq//ebjd/D50fMpqr/sX39HCTpZr8sSAkBICQEgJASAkBICQEgIzrl1x649ceuPXHrj1x649ceuPXHrj1x66XTXHrj1x649ceuPXHrj1x649ceuPXHrMNPegthWwrYVsK2FbCthWwrYVsK1YLh1p5RWpbxRXPe8JlQ3gNC0YVsK2FbCthWwrYVsK2FbCt... | [{"identifier": "A", "content": "$$5 \\sqrt{3} N$$\n"}, {"identifier": "B", "content": "$$\\frac{5 \\sqrt{3}}{2} N$$\n"}, {"identifier": "C", "content": "$$10 \\mathrm{~N}$$\n"}, {"identifier": "D", "content": "$$25 \\sqrt{3} N$$"}] | ["A"] | null | <p>$$\begin{aligned}
\mathrm{f}_{\mathrm{K}} & =\mu \mathrm{mg} \cos \theta \\
& =0.1 \times \frac{50 \times \sqrt{3}}{2} \\
& =2.5 \sqrt{3} \mathrm{~N}
\end{aligned}$$</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsiimidj/c7ed607d-e180-4d33-85a1-804c49805319/9e93d970-c96a-1... | mcq | jee-main-2024-online-31st-january-evening-shift | 11,690 |
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