Two billiard balls A and B each of mass 50 g and moving in opposite directions with speed of `5 m//s` each, collide and rebound with the same speed if the collision lasts for `10^(-3)` s which of the following statement(s) is (are) true?

Options

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

Answer

C, D

Explanation

Given `" " m_(1) = m_(2) 50(g) = (50)/(1000) kg = (1)/(20) kg `
Initial velocity (u) = `u_(1) = u_(2) = 5m//s`
Final velocity (v) = `v_(1) = v_(2) =- 5 m//s`
Time duration of collision = `10^(-3) s `
Change in linear momentum = m (v-u)
= `(1)/(20) [-5-5] = - 0.5 N-s`.
Force = `("Impulse")/("Time") = ("Change in momentum")/(10^(-3) s)`
= `(0.5)/(10^(-3)) = 500 N`
Impulsive and force are opposite in directions.