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 impluse imparated to each ball is `0.25kg ms^(-1)` and the force on each ball is `250N`.
B. The impluse imparated to each ball is `0.25 kg ms^(-1)` and the force exerted on each ball is `25xx10^(-5)N`.
C. The impluse imparated to each ball is `0.5Ns`.
D. The impluse and the force on each ball are equal in magnitude and opposite in direction.

Answer

C, D

Explanation

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