Question

Two billiard balls $A$ and $B$, each of mass $50g$ and moving in opposite directions with speed of $5m/s$ 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 $0.25kgm/s$ and the force on each ball is $250N.$
• B. The impulse and the force on each ball are equal in magnitude and opposite in direction.
  
• C. The impulse imparted to each ball is $0.25kgm/s$ and the force exerted on each ball is $25\times {10}^{–5}N.$
• D. The impulse imparted to each ball is $0.5Ns.$

Answer 1

Answer: (B), (D)

The impulse imparted to each ball is $0.5Ns.$

Step 1: Find initial momentum of each ball.

Formula used: $p=mv$

Given, mass of each ball $m=50g=\frac{50}{1000}kg=0.05kg$

Initial velocity of the balls, $u=5m/s$

So, initial momentum of each ball, $p_i=mu$

$p_i=0.05\times 5=0.25Ns$

Step 2: Find final momentum of each ball.

Formula used: $p=mv$

Given, after collision each ball rebounds with the same speed,

Final speed of each ball,$v=-5m/s$

So, final momentum of each ball,$p_f=mv$

$p_f=0.05\times -5=-0.25Ns$

Step 3: Find impulse of each ball.

Definition: Impulse; Impulse describes the effect of force acting over time to change the momentum of an object.

Formula used:$J=△p$

As we know, impulse(J)= change in momentum$\left(△p\right)$

$J=p_i-p_f=0.25+0.25$

$J=0.5Ns$

Step 4: Find force on each ball.

Formula used: $J=△p=F_t$

Given, time taken in the collision, $t={10}^{-3}s$

So, force on each ball, $F=△p_t$

$F=\frac{0.5}{{10}^{-3}}=500N$

As initially balls are moving in opposite direction so impulse and force on each ball are opposite in direction and same in magnitude.

Final answer: (c), (d)