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 k g

${m}=0.05 \mathrm{~kg}$ and

v = 5 m / s

${v}=5 \mathrm{~m} / \mathrm{s}$
Hence we have initial momentum of each ball is given by;

\Rightarrow p = m v = 0.05 \times 5 = 0.25 k g - {m s}^{- 1}

$\Rightarrow {p}={mv}=0.05 \times 5=0.25 \mathrm{~kg}\text- \mathrm{ms}^{-1}$
After the collision, both balls will move in opposite directions
Hence, we have the final momentum of each ball is given by;

\Rightarrow p^{'} = - m v = - 0.05 \times 5 = - 0.25 k g - {m s}^{- 1}

$\Rightarrow {p}^{\prime}=-{mv}=-0.05 \times 5=-0.25 \mathrm{~kg}\text- \mathrm{ms}^{-1}$
Now the impulse is the change in momentum given by;

\Rightarrow I = p^{'} - p = - 0.25 - 0.25 = - 0.5 k g - {m s}^{- 1} .

$\Rightarrow I=p^{\prime}-p=-0.25-0.25=-0.5 \mathrm{~kg}\text-\mathrm{ms}^{-1}.$
Hence, option (3) is the correct answer.

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