On a frictionless surface, a block of mass \(M\) moving at speed \(v\) collides elastically with another block of the same mass \(M\) which is initially at rest. After the collision, the first block moves at an angle \(\theta\) to its initial direction and has a speed \(\frac{v}{3}\). The second block’s speed after the collision will be:
1. \(\frac{2\sqrt{2}}{3}v\)
2. \(\frac{3}{4}v\)
3. \(\frac{3}{\sqrt{2}}v\)
4. \(\frac{\sqrt{3}}{2}v\)

Subtopic:  Collisions |
 66%
From NCERT
NEET - 2015
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A body of mass (\(4m\)) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (\(m\)) move perpendicular to each other with equal speeds (\(u\)). The total kinetic energy generated due to explosion is:

1. \(mu^2\) 2. \(1.5~mu^2\)
3. \(2~mu^2\) 4. \(3~mu^2\)

Subtopic:  Concept of Work |
 61%
From NCERT
AIPMT - 2014
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A uniform force of \((3 \hat{i} + \hat{j})\) newton acts on a particle of mass \(2\) kg. Hence the particle is displaced from position \((2 \hat{i} + \hat{k})\) meter to position \((4 \hat{i} + 3 \hat{j} - \hat{k})\) meter. The work done by the force on the particle is:

1. \(6\) J 2. \(13\) J
3. \(15\) J 4. \(9\) J

Subtopic:  Concept of Work |
 80%
From NCERT
AIPMT - 2013
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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass \(1\) kg moves with a speed of \(12\) ms–1 and the second part of mass \(2\) kg moves with \(8\) ms–1 speed. If the third part flies off with \(4\) ms–1 speed, then its mass is:
1. \(5\) kg
2. \(7\) kg
3. \(17\) kg
4. \(3\) kg
Subtopic:  Collisions |
 69%
From NCERT
AIPMT - 2013
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The potential energy of a particle in a force field is \(U=\)Ar2-Br where \(A\) and \(B\) are positive constants and \(r\) is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

1. \(\frac{B}{A}\) 2. \(\frac{B}{2A}\)
3. \(\frac{2A}{B}\) 4. \(\frac{A}{B}\)

Subtopic:  Potential Energy: Relation with Force |
 77%
From NCERT
AIPMT - 2012
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Two spheres \(A\) and \(B\) of masses \(m_1\) and \(m_2\), respectively, collide. \(A\) is at rest initially and \(B\) is moving with velocity \(v\) along the \(x\)-axis. After the collision, \(B\) has a velocity \(\frac{v}{2}\) in a direction perpendicular to the original direction. The mass \(A\) moves after collision in the direction:

1. same as that of \(B\).
2. opposite to that of \(B\).
3. \(\theta = \text{tan}^{-1}\left(\frac{1}{2} \right)\) to the positive \(x\)-axis.
4. \(\theta = \text{tan}^{-1}\left(\frac{-1}{2} \right )\) to the positive \(x\)-axis.
Subtopic:  Collisions |
From NCERT
AIPMT - 2012
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The potential energy of a system increases if work is done:

 
1. by the system against a conservative force
2. by the system against a non-conservative force
3. upon the system by a conservative force
4. upon the system by a non-conservative force

Subtopic:  Potential Energy: Relation with Force |
 67%
From NCERT
AIPMT - 2011
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Force \(F\) on a particle moving in a straight line varies with distance \(d\) as shown in the figure. The work done on the particle during its displacement of \(12\) m is: 

              

1. \(21\) J
2. \(26\) J
3. \(13\) J
4. \(18\) J

Subtopic:  Work Done by Variable Force |
 72%
From NCERT
AIPMT - 2011
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A ball moving with velocity 2 ms-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms-1) after the collision will be:

1. 0, 1

2. 1, 1

3. 1, 0.5

4. 0, 2

Subtopic:  Collisions |
 68%
From NCERT
AIPMT - 2010
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An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms-1. The mass per unit length of water in the pipe is 100 kg m-1.What is the power of the engine?

1. 400 W

2. 200 W

3. 100 W

4. 800 W

Subtopic:  Power |
From NCERT
AIPMT - 2010
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