A ball is thrown vertically downward from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision, and rebounds to the same height. The initial velocity \(v_0\) is: 
(Take, \(g=10~\mathrm{ms^{-2}}\))
1. \(14\) ms-1
2. \(20\) ms-1
3. \(28\) ms-1
4. \(10\) ms-1

Subtopic:  Gravitational Potential Energy |
 64%
From NCERT
NEET - 2015
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Two similar springs \(P\) and \(Q\) have spring constants \(k_P\) and \(k_Q\), such that \(k_P>k_Q\). They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs \(W_P\) and \(W_Q\) are related as, in case (a) and case (b), respectively:

1. \(W_P=W_Q;~W_P>W_Q\)
2. \(W_P=W_Q;~W_P=W_Q\)
3. \(W_P>W_Q;~W_P<W_Q\)
4. \(W_P<W_Q;~W_P<W_Q\)
Subtopic:  Elastic Potential Energy |
 72%
From NCERT
NEET - 2015
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A block of mass \(10\) kg, moving in the x-direction with a constant speed of \(10\) ms-1 is subjected to a retarding force \(F=0.1x\) J/m during its travel from \(x = 20\) m to \(30\) m. Its final kinetic energy will be:
1. \(475\) J
2. \(450\) J
3. \(275\) J
4. \(250\) J

Subtopic:  Work Energy Theorem |
 72%
From NCERT
NEET - 2015
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A particle of mass \(m\) is driven by a machine that delivers a constant power of \(k\) watts. If the particle starts from rest, the force on the particle at time \(t\) is:
1. \( \sqrt{\frac{m k}{2}} t^{-1 / 2} \)
2. \( \sqrt{m k} t^{-1 / 2} \)
3. \( \sqrt{2 m k} t^{-1 / 2} \)
4. \( \frac{1}{2} \sqrt{m k} t^{-1 / 2}\)

Subtopic:  Power |
 54%
From NCERT
NEET - 2015
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Two particles of masses \(m_1\) and \(m_2\) move with initial velocities \(u_1\) and \(u_2\) respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy \(E\). If the final velocities of particles are \(v_1\) and \(v_2\), then we must have:

1. \(m_1^2u_1+m_2^2u_2-E = m_1^2v_1+m_2^2v_2\)
2. \(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2= \frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
3. \(\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2-E= \frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2\)
4. \(\frac{1}{2}m_1^2u_1^2+\frac{1}{2}m_2^2u_2^2+E = \frac{1}{2}m_1^2v_1^2+\frac{1}{2}m_2^2v_2^2\)
Subtopic:  Collisions |
 62%
From NCERT
NEET - 2015
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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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A particle with total energy \(E\) is moving in a potential energy region \(U(x).\) The motion of the particle is restricted to the region where:
1. \(U(x)<E\)
2. \(U(x)=0\)
3. \(U(x)\leq E\)
4. \(U(x)> E\)
Subtopic:  Conservation of Mechanical Energy |
From NCERT
NEET - 2013
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