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  • Two billiard balls A and B, each of mass 50g and moving in opposite directions with speed of 5m s^-1 each, collide and rebound with the same speed. If the collision lasts for 10^-3 s, which of the following statements are true?

Two billiard balls A and B, each of mass 50g and moving in opposite directions with speed of 5m s-1 each, collide and rebound with the same speed. If the collision lasts for 10^{-3} s, which of the following statements are true?
(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 × 10-5 N.
(c) The impulse imparted to each ball is 0.5 Ns.
(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Answers (1)

The correct answer is:

(c) The impulse imparted to each ball is 0.5 Ns.

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

Let m be the mass of each ball, m = 0.05 kg

Let v be the speed of each ball, v = 5m/s

 We know that the initial momentum of each ball will be

\overrightarrow{p_{i}}=m\overrightarrow{v}

\overrightarrow{p_{i}}=(0.05)(5)=0.25kgms^{-1}

= 0.25 N-s             ……….. (i)

 After the collision, on rebounding, the direction of the velocity of each ball is reversed; hence, the final momentum of each ball will be

\overrightarrow{p}=m(-\overrightarrow{v})

=- 0.25 N-s.

Hence, opt (d) is verified.

Thus, it is clear that impulse imparted to each ball is equal to change in momentum of each ball

= p_{f} - p_{i}

= - 0.25 – (0.25)

= -0.50 kg ms-1

= -0.50 N-s

Here opt (c) is also verified.

 

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infoexpert24

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