Two billiard balls A and B, each of mass 50 kg and moving in oppsite direction with speed of `5ms^-1` each, collide and rebound with the same speed. If the collision lasts for `10^-3s`, which of the follwing statements are true?

Options

A. The impulse imparted to each ball is `0.25kg ms^(-1)` and the force on each ball is `250N`
B. The impulse imparted to each ball is `0.25kg ms^(-1)` and the force exerted on each on each ball is `25 xx 10^(-5)N
C. The impulse imparted to each ball is `0.5Ns`
D. The impulse and the force on each ball are equal in magnitude and opposite in direction

Answer

c,d

Explanation

Here, `m_(1) = m_(2) = m = 50 g = (50)/(100)kg = (1)/(20)kg`
initial vel `(u) = u_(1) = u_(2) = 5m//s` final vel `(upsilon) = upsilon_(1) = upsilon_(2) = - 5m//s, t = 10^(-3) s`
Impulse imparted to each ball = change in linear momentum of each ball
`m (upsilon - u) = (1)/(2) (-5 - 5) = - 0.5Ns`
Force ` =("Impulse")/(t) = (0.5)/(10^(-3) = 500N`
The impulse and force on each ball are equal in magnitude and opposite in direction .