
If only conservative forces are working in the system and we apply some external force
A)
\[{{W}_{ext}}=\Delta U\](always) done
clear
B)
\[{{W}_{\text{conservative}}}=\Delta U\](always) done
clear
C)
\[{{W}_{ext}}=\Delta U+\Delta KE\] (always) done
clear
D)
\[{{W}_{\operatorname{co}nservative}}=\Delta KE\] done
clear
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The force acting on a body moving along xaxis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at: 

A)
\[x={{x}_{1}}\] done
clear
B)
\[x={{x}_{2}}\] done
clear
C)
both \[{{x}_{1}}\]and \[{{x}_{2}}\] done
clear
D)
neither \[{{x}_{\text{1}}}\]nor \[{{x}_{2}}\] done
clear
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Two identical balls A and B are released from the positions shown in figure. They collide elastically on horizontal portion\[M/N\]. All surfaces are smooth. The ratio of heights attained by A and B after collision will be
A)
\[1:4\] done
clear
B)
\[2:1\] done
clear
C)
\[4:13\] done
clear
D)
\[2:5\] done
clear
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A body of mass M splits into two parts \[\alpha \] and \[(1\alpha )\] M by an internal explosion which generates kinetic energy T. After explosion if the two parts move in the same direction as before, their relative speed will be 
A)
\[\sqrt{\frac{T}{(1\alpha )M}}\] done
clear
B)
\[\sqrt{\frac{2T}{\alpha (1\alpha )M}}\] done
clear
C)
\[\sqrt{\frac{T}{2(1\alpha )M}}\] done
clear
D)
\[\sqrt{\frac{2T}{(1a)M}}\] done
clear
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A simple pendulum with a bob of mass 'm' oscillates from A to C and back to A such that PB is H. If the acceleration due to gravity is 'g', then the velocity of the bob as it passes through B is
A)
zero done
clear
B)
\[2\,gH\] done
clear
C)
\[mgH\] done
clear
D)
\[\sqrt{2gH}\] done
clear
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A certain system has potential energy given by the function \[U(x)=a{{x}^{2}}+b{{x}^{4}}\]with constants, a, b > 0. Which of the following value of x is an unstable equilibrium point?
A)
0 done
clear
B)
\[\sqrt{a/2b}\] done
clear
C)
\[\sqrt{a/2b}\] done
clear
D)
\[\sqrt{a/b}\] done
clear
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Two springs of force constant 100 N/m and 150 N/m are in series as shown. The block is pulled by a distance of 2.5 cm to the right from equilibrium position. What is the ratio of work done by the spring at left to the work done by the spring at right. 

A)
\[\frac{3}{2}\] done
clear
B)
\[\frac{2}{3}\] done
clear
C)
0.2 done
clear
D)
None of these done
clear
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A force \[\overset{\to }{\mathop{F}}\,=k(y\hat{i}+x\hat{j})\] acts on a particle moving in the x y plane. Starting from the origin, the particle is taken along the positive xaxis to the point (a, 0) and then parallel to the j'axis to the point (a, a). The total work done by the force is
A)
\[2k{{a}^{2}}\] done
clear
B)
\[2\,\,k{{a}^{2}}\] done
clear
C)
\[k{{a}^{2}}\] done
clear
D)
\[k{{a}^{2}}\] done
clear
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A uniform rectangular marble slab is 3.4 m long and 2.0 m wide. It has a mass of 180 kg. If it is originally lying on the flat ground, how much work is needed to stand it on an end?
A)
2.0 kJ done
clear
B)
3.0 J done
clear
C)
3.0 kJ done
clear
D)
3000 kJ done
clear
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An inertial frame S' is moving with a constant velocity with respect to another inertial frame s. Then
A)
kinetic energy of an object when viewed from S and S' will be different done
clear
B)
work done on an object when evaluated in frame S and S' will be different done
clear
C)
work energy theorem is valid in all inertial frames done
clear
D)
all of these done
clear
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Body of mass m moving with a velocity\[v\]in the \[+\text{ }ve\]X direction collides with a body of mass M moving with a velocity V in the \[+\text{ }ve\]Y direction. The collision is perfectly inelastic. Mark out the correct statement(s) w.r.t. this situation.
A)
The magnitude of momentum of the composite body is\[\sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}}\] done
clear
B)
The composite body moves in a direction making an angle \[\theta ={{\tan }^{1}}\left( \frac{MV}{mv} \right)\]with \[+\text{ }ve\]Xaxis. done
clear
C)
The loss of kinetic energy due to collision done
clear
D)
All of the above done
clear
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A chain of mass m and length\[l\]lies on the surface of a rough sphere of radius\[R(>1)\] such that one end of chain is at the top most point of sphere. The chain is held at rest because of friction. The gravitational potential energy of the chain in this position (considering the horizontal diameter of sphere as reference level for gravitational potential energy), is
A)
\[\frac{mg{{R}^{2}}}{l}\] done
clear
B)
\[\frac{mg{{R}^{2}}}{l}\sin \left( \frac{l}{R} \right)\] done
clear
C)
\[\frac{mg{{R}^{2}}}{l}\cos \left( \frac{l}{R} \right)\] done
clear
D)
None of these done
clear
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A ball of mass m moving with velocity V makes a headon elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V, the positive velocities of the two balls after collision are
A)
\[V\]and 2V done
clear
B)
2V and \[V\] done
clear
C)
V and \[2V\] done
clear
D)
\[2V\]and V done
clear
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A block of mass m moving with a velocity \[{{v}_{0}}\]on a smooth horizontal floor collides with a light spring of stiffhess k that is rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is F, then
A)
\[F\propto \sqrt{m}\] done
clear
B)
\[F\propto \sqrt{k}\] done
clear
C)
\[F\propto {{v}_{0}}\] done
clear
D)
None of these done
clear
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A constant power P is applied to a particle of mass m. The distance traveled by the particle when its velocity increases from \[{{v}_{1}}\], to \[{{v}_{2}}\]is (neglect friction)
A)
\[\frac{m}{3P}(v_{2}^{3}v_{1}^{3})\] done
clear
B)
\[\frac{m}{3P}({{v}_{2}}{{v}_{1}})\] done
clear
C)
\[\frac{3p}{m}(v_{2}^{2}v_{1}^{2})\] done
clear
D)
\[\frac{m}{3P}(v_{2}^{2}v_{1}^{2})\] done
clear
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A body of mass m accelerates uniformly from rest to a speed \[\left( \lambda \right)\]in time \[\infty \]. The work done on the body till any time t is
A)
\[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)\] done
clear
B)
\[\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}_{0}}}{t} \right)\] done
clear
C)
\[mv_{0}^{2}\left( \frac{t}{{{t}_{0}}} \right)\] done
clear
D)
\[mv_{0}^{2}{{\left( \frac{t}{{{t}_{0}}} \right)}^{3}}\] done
clear
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A particle is displaced from \[x=6\text{ }m\] to \[x=+6\text{ }m\]. A force F acting on the particle during its motion in shown in figure. Graph between work done by this force (W) and displacement (x) should be 

A)
B)
C)
D)
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During the compression of the spring, the net work done on the block is
A)
Positive done
clear
B)
Negative done
clear
C)
Zero done
clear
D)
Cannot say done
clear
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Two blocks A and B of masses m and 2m placed on a smooth surface are travelling in opposite directions with velocities of 6 m/s and 4 m/s respectively. A perfectly elastic spring is attached to block A. If after collision, velocity of A is \[\frac{2}{3}\,\,m/s\] towards right , then velocity of block B would be 

A)
\[\frac{4}{3}\,m/s\] towards left done
clear
B)
\[\frac{16}{3}\,m/s\] towards left done
clear
C)
\[\frac{28}{3}\,m/s\] m/s towards left done
clear
D)
4 m/s towards left done
clear
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The ratio of masses of two balls is 2 : 1 and before collision the ratio of their velocities is 1 : 2 in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If e = (5/6), the ratio of speed of each ball before and after collision would be
A)
(5/6) times done
clear
B)
Equal done
clear
C)
Not related done
clear
D)
Double for the first ball and half for the second ball done
clear
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Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{6}\] done
clear
D)
\[\frac{\sqrt{3}}{2}\] done
clear
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A ball of mass m hits a wall with a speed v making an angle \[\frac{5g}{14}\] with the normal. If the coefficient is e, the direction and magnitude of the velocity of ball after reflection from the wall will respectively be 
A)
\[{{\tan }^{1}}\left( \frac{\tan \theta }{e} \right),\,v\sqrt{{{\sin }^{2}}\theta +{{e}^{2}}{{\cos }^{2}}\theta }\] done
clear
B)
\[{{\tan }^{1}}\left( \frac{e}{\tan \theta } \right),\frac{1}{v}\sqrt{{{e}^{2}}{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }\] done
clear
C)
\[{{\tan }^{1}}(e\tan \theta ),\frac{v}{e}\tan \theta \] done
clear
D)
\[{{\tan }^{1}}(e\tan \alpha ),v\sqrt{{{\sin }^{2}}\theta +{{e}^{2}}}\] done
clear
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A person brings a mass of 1 kg from infinity to a point 'A'. Initially the mass was at rest but it moves at a speed of 2m/s as it reached A. The work done by the person on the mass is 3J. The potential at 'A' is:
A)
\[3J/kg\] done
clear
B)
\[2J/kg\] done
clear
C)
\[5J/kg\] done
clear
D)
none of these done
clear
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A bullet of mass m moving vertically upwards instantaneously with a velocity 'u' hits the hanging block of mass 'm' and gets embedded in it, as shown in the figure. The height through which the block rises after the collision, (assume sufficient space above block) is: 

A)
\[{{\text{u}}^{2}}/2g\] done
clear
B)
\[{{\text{u}}^{2}}/g\] done
clear
C)
\[{{\text{u}}^{2}}/8g\] done
clear
D)
\[{{\text{u}}^{2}}/4g\] done
clear
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A particle of mass m collides inelastically with another particle of mass 3m which is at rest. After the collision first particle comes to rest. Then choose the wrong answer 

A)
coefficient of restitution between the particles is \[1/3\] done
clear
B)
loss of kinetic energy during collision is \[\left( 1/3 \right)m{{v}^{2}}\] done
clear
C)
velocity of second particle after collision is\[v/3\]. done
clear
D)
all of these done
clear
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Two masses connected by a mass less spring .are placed on a horizontal smooth surface. The spring is initially compressed by 3 cm. The system is released from rest. The velocity (in m/s) of the 2 kg mass, when spring attains natural length is to 

A)
\[\sqrt{\frac{3}{2}}\] done
clear
B)
\[\sqrt{\frac{2}{3}}\] done
clear
C)
\[\frac{3}{2}\] done
clear
D)
\[\sqrt{3}B=\left( 1/5\text{ }x\text{ }30 \right)\] done
clear
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A body of mass 1 kg initially at rest explodes and breaks into three fragments of masses in the ratio 1 : 1 : 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 30 m/sec each. What is the velocity of the heavier fragment?
A)
\[10\sqrt{2}\,m/s\] done
clear
B)
\[15\sqrt{2}\,m/s\] done
clear
C)
\[5\sqrt{2}\,\,m/s\] done
clear
D)
\[20\sqrt{2}\,\,m/s\] done
clear
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A block of mass m is pulled by a constant power P placed on a rough horizontal plane. The friction coefficient between the block and the surface is \[\text{I}{{\text{F}}_{\text{3}}}\]. Maximum velocity of the block will be
A)
\[\frac{\mu p}{mg}\] done
clear
B)
\[\frac{\mu mg}{p}\] done
clear
C)
\[\mu mgp\] done
clear
D)
\[\frac{p}{\mu mg}\] done
clear
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Block 1 and Block 2 are again released from \[h=1.2\text{ }m.\] Block 1 flies off the track end at 30° and Block 2 at \[45{}^\circ \]. Their speeds when they hit the floor 1 meter below the track end:
A)
are smaller for Block 1 than Block 2. done
clear
B)
are larger for Block 1 than Block 2. done
clear
C)
are the same for Block 1 and Block 2. done
clear
D)
depend on mass and angle, so the question cannot be answered. done
clear
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A body of mass m dropped from a certain height strikes a light vertical fixed spring of stiffness k. The height of its fall before touching the spring if the maximum compression of the spring is equal to \[\frac{3mg}{k}\] is:
A)
\[\frac{KQ}{R}\] done
clear
B)
\[\frac{KQ}{\ell }\] done
clear
C)
\[\frac{KQ}{\sqrt{{{R}^{2}}+{{\ell }^{2}}}}\] done
clear
D)
\[\frac{mg}{4K}\] done
clear
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The particle is released from a height h. At a certain height, its KE is two times its potential energy Height and speed of the particle at that instant are
A)
\[\frac{h}{3},\,\frac{\sqrt{2gh}}{3}\] done
clear
B)
\[\frac{h}{3},\,\frac{\sqrt{gh}}{3}\] done
clear
C)
\[\frac{2h}{3},\,\frac{\sqrt{2gh}}{3}\] done
clear
D)
\[\frac{h}{3},\,\sqrt{2gh}\] done
clear
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The potential energy function associated with the force \[\vec{F}=4xy\hat{i}+2{{x}^{2}}\hat{j}\] is:
A)
\[U=2{{x}^{2}}y\] done
clear
B)
\[U=2{{x}^{2}}y+\] constant done
clear
C)
\[U=2{{x}^{2}}y+\] constant done
clear
D)
not defined done
clear
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A body of mass m is released from a height h to a scale pan hung from a spring as shown in figure. The spring constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is 

A)
\[\frac{mg}{k}\sqrt{\left( 1+\frac{2\,hk}{mg} \right)}\] done
clear
B)
\[\frac{mg}{k}\] done
clear
C)
\[\frac{mg}{k}\left[ 1+\sqrt{\left( 1+\frac{2\,hk}{mg} \right)} \right]\] done
clear
D)
\[\frac{mg}{k}\frac{mg}{k}\left[ \sqrt{\left( 1\frac{2hk}{mg} \right)} \right]\] done
clear
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DIRECTION: In the following questions, more than one of the answers given are correct. Select the correct answers and mark it according to the following codes: 
Codes 
A man pushes a wall and fails to displace it. Choose incorrect statements related to his work 
(1) Negative work 
(2) Positive but not maximum work 
(3) Maximum work 
(4) No work at all 
A)
1, 2 and 3 are correct done
clear
B)
1 and 2 are correct done
clear
C)
2 and 4 are correct done
clear
D)
1 and 3 are correct done
clear
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DIRECTION: In the following questions, more than one of the answers given are correct. Select the correct answers and mark it according to the following codes: 
Codes 
Choose the correct options  
(1) The work done by forces may be equal to change in kinetic energy 
(2) The work done by forces may be equal to change in potential energy 
(3) The work done by forces may be equal to change in total energy 
(4) The work done by forces must be equal to change in potential energy. 
A)
1, 2 and 3 are correct done
clear
B)
1 and 2 are correct done
clear
C)
2 and 4 are correct done
clear
D)
1 and 3 are correct done
clear
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