Ncert Exercises & Solutions

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

(a)	the impulse imparted to each ball is \(0.25~\text{kg-ms}^{-1}\) and the force on each ball is \(250~\text N\)
(b)	the impulse imparted to each ball is \(0.25~\text{kg-ms}^{-1}\) and the force exerted on each ball is \(25\times 10^{-5}~\text N\)
(c)	the impulse imparted to each ball is \(0.5~\text{N-s}\)
(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) and (c) only
2.	(a) and (b) only
3.	(c) and (d) only
4.	(b) and (c) only

Hint: Apply the concept of conservation of momentum.

Step: Find the final velocities of the balls.

We are given that, \({m}=0.05 \mathrm{~kg}\) and \({v}=5 \mathrm{~m} / \mathrm{s}\)
Hence we have initial momentum of each ball is given by;
\(\Rightarrow {p}={mv}=0.05 \times 5=0.25 \mathrm{~kg}\text- \mathrm{ms}^{-1}\)
After the collision, both balls will move in opposite directions
Hence, we have the final momentum of each ball is given by;
\(\Rightarrow {p}^{\prime}=-{mv}=-0.05 \times 5=-0.25 \mathrm{~kg}\text- \mathrm{ms}^{-1}\)
Now the impulse is the change in momentum given by;
\(\Rightarrow I=p^{\prime}-p=-0.25-0.25=-0.5 \mathrm{~kg}\text-\mathrm{ms}^{-1}.\)
Hence, option (3) is the correct answer.

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