A mass of \(5~\text {kg}\) is moving along a circular path of radius \(1~\text {m}\). If the mas moves with \(300~\text {rev/min}\), its kinetic energy would be
1. \(250 \pi^2~\text{J}\)
2. \(100 \pi^2~\text{J}\)
3. \(5 \pi^2~\text{J}\)
4. \(0\)
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A cricket ball of mass \(150~\text{g}\) moving with a speed of \(126~\text{km/h}\) hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remains in contact for \(0.001~\text{s}\), the force that the batsman had to apply to hold the bat firmly at its place would be:
1. \(10.5~\text{N}\)
2. \(21~\text{N}\)
3. \(1.05\times10^{4}~\text{N}\)
4. \(2.1\times 10^{4}~\text{N}\)
A man of mass \(m,\) standing at the bottom of the staircase, of height \(L,\) climbs it and stands at its top.
(a) | work done by all forces on man is equal to the rise in potential energy \(mgL.\) |
(b) | work done by all forces on man is zero. |
(c) | work done by the gravitational force on man is \(mgL.\) |
(d) | the reaction force from a step does no work because the point of the application of the force does not move while the force exists. |
Choose the correct option:
1. (a), (d)
2. (a), (c)
3. (b), (d)
4. (a), (b), (c)
A bullet of mass \(m\) fired at \(30^\circ\) to the horizontal leaves the barrel of the gun with a velocity \(v.\) The bullet hits a soft target at a height \(h\) above the ground while it is moving downward and emerge out with half the kinetic energy it had before hitting the target. Consider the following statements.
(a) | the velocity of the bullet will be reduced to half its initial value. |
(b) | the velocity of the bullet will be more than half of its earlier velocity. |
(c) | the bullet will continue to move along the same parabolic path. |
(d) | the bullet will move in a different parabolic path. |
(e) | the bullet will fall vertically downward after hitting the target. |
(f) | the internal energy of the particles of the target will increase. |
Which of the above-given statement(s) is/are correct in respect of the bullet after it emerges out of the target?
1. (a), (c), (f)
2. (a), (d), (f)
3. (b), (d, (f)
4. (a), (b), (c)
1. | same as the same force law is involved in the two experiments. |
2. | less for the case of a position, as the position moves away more rapidly and the force on it weakens. |
3. | more for the case of a position, as the position moves away from a larger distance. |
4. | same as the work done by charged particle on the stationary proton. |
A man squatting on the ground gets straight up and stands. The force of reaction of the ground on the man during the process is
1. | constant and equal to mg in magnitude. |
2. | constant and greater than mg in magnitude. |
3. | variable but always greater than mg. |
4. | at first, greater than mg and later becomes equal to mg. |
A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. | \(+2000\) J | 2. | \(-200\) J |
3. | zero | 4. | \(-20000\) J |