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 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. \(2.1\times 10^{4}~\text{N}\)

During an inelastic collision between two bodies, which of the following quantities always remain conserved?

Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same time moving initially with a speed \(v\) as shown in the figure.

If the collision is elastic, which of the following (figure) is a possible result after collision?

1.		2.
3.		4.

Two blocks \(M_1\)​ and \(M_2\)​ having equal mass are free to move on a horizontal frictionless surface. \(M_2\)​ is attached to a massless spring as shown in figure. Initially, \(M_2​\) is at rest and \(M_1​\) is moving toward \(M_2\)​ with speed \(v \) and collides head-on with \(M_2.\) 

      
Consider the following given statements: