Two billiard balls A and B, each of mass 50g and moving in opposite directions with a speed of 5 m/s each, collide and rebound at the same speed. If the collision lasts for ${10}^{-3}$ s,

(a) The impulse imparted to each ball is 0.25 $kg-m{s}^{-1}$ and the force on each ball is 250 N

(b) The impulse imparted to each ball is 0.25 $kg-m{s}^{-1}$ and the force exerted on each ball is 25 x ${10}^{-\mathrm{5 }}$N

(c) The impulse imparted to each ball is 0.5 N-s

(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Which of the following statement(s) is/are true?

1. (a, c)

2. (a, b)

3. (c, d)

4. (b, c)

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shown the displacement-time curve for its motion?

1.		2.
3.		4.

Which of the diagrams shown in the figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?

1.		2.
3.		4.

Which of the diagrams shown in the figure represents the variation of to mechanical energy of a pendulum oscillating in the air as a function of time.
 

1.		2.
3.		4.

A mass of 5 kg is moving along a circular path of radius 1 m. If the mas moves with 300 rev/min, its kinetic energy would be
 

1. 250${\mathrm{\pi }}^2$

2. 100${\mathrm{\pi }}^2$

3. 5${\mathrm{\pi }}^2$

4. 0

In a shotput event, an athlete throws the shotput of mass \(10\) kg with an initial speed of \(1\) m/s at \(45^\circ\) from a height \(1.5\) m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be \(10\) m/${\mathrm{s}}^2$, the kinetic energy of the shotput when it just reaches the ground will be:
1. \(2.5\) J
2. \(5.0\) J
3. \(52.5\) J
4. \(155.0\) J

A cricket ball of mass 150 g moving with a speed of 126 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 0.001s, the force that the batsman had to apply to hold the bat firmly at its place would be

1. 10.5 N   
2. 21 N   
3. 1.05 x ${10}^4$ N   
4. 2.1 x ${10}^4$ N

A man of mass \(m,\) standing at the bottom of the staircase, of height \(L,\) climbs it and stands at its top.

Choose the correct option:
1. (a, d)
2. (a, c)
3. (b, d)
4. (a, b, c)