The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, potential energy stored in it will be: 
1. \(16U\) 2. \(2U\)
3. \(4U\) 4. \(8U\)
Subtopic:  Elastic Potential Energy |
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A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels \(24\) cm through the block along its length horizontally, velocity of bullet becomes \(u/3\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
1. \(30\) cm
2. \(27\) cm
3. \(24\) cm
4. \(28\) cm
Subtopic:  Work Energy Theorem |
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A bullet of mass \(m\) hits a block of mass \(M\) elastically. The transfer of energy is the maximum, when:
1. \(M=m\)
2. \(M=2m\)
3. \(M\ll m\)
4. \(M\gg m\)
Subtopic:  Collisions |
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A particle moves with a velocity \((5\hat i-3\hat j+6\hat k)\) ms-1 horizontally under the action of constant force \((10\hat i+10\hat j+20\hat k)\) N. The instantaneous power supplied to the particle is:
1. \(200\) W
2. zero
3. \(100\) W
4. \(140\) W
Subtopic:  Power |
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The energy that will be ideally radiated by a \(100\) kW transmitter in \(1\) hour is:
1. \(1\times 10^{5}\) J
2. \(36\times 10^{7}\) J
3. \(36\times 10^{4}\) J
4. \(36\times 10^{5}\) J
Subtopic:  Power |
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An electric lift with a maximum load of \(2000\) kg (lift+passengers) is moving up with a constant speed of \(1.5\) ms–1. The frictional force opposing the motion is \(3000\) N. The minimum power delivered by the motor to the lift in watts is: (Take \(g=10\) ms–2)
1. \(23500\) 2. \(23000\)
3. \(20000\) 4. \(34500\)
Subtopic:  Power |
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A particle of mass \(4M\) kg at rest splits into two particles of mass \(M\) and \(3M.\) The ratio of the kinetic energies of mass \(M\) and \(3M\) would be:

1. \(3:1\) 2. \(1:4\)
3. \(1:1\) 4. \(1:3\)
Subtopic:  Collisions |
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A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
                 

1. \(u\sqrt{\dfrac{m}{k}}\) 2. \(4u\sqrt{\dfrac{m}{k}}\)
3. \(2u\sqrt{\dfrac{m}{k}}\) 4. \(\dfrac12u\sqrt{\dfrac{k}{m}}\)
Subtopic:  Elastic Potential Energy |
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A gravitational field is present in a region and a mass is shifted from \(A\) to \(B\) through different paths as shown. If \(W_1\), \(W_2\) and \(W_3\) represent the work done by the gravitational force along their respective paths, then:
1. \(W_1=W_2=W_3\) 2. \(W_1>W_2>W_3\)
3. \(W_1>W_3>W_2\) 4. \(W_1<W_2<W_3\)
Subtopic:  Gravitational Potential Energy |
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Given below are two statements: 
Assertion (A): When a firecracker (rocket) explodes in mid-air, its fragments fly in such a way that they continue moving in the same path, which the firecracker would have followed, had it not exploded.
Reason (R): Explosion of cracker (rocket) occurs due to internal forces only and no external force acts for this explosion.
 
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. (A) is false but (R) is true.
Subtopic:  Collisions |
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