Three identical balls, ball I, ball II and ball III are placed on a smooth floor on a straight line at the separation of `10m` between balls as shown in figure. Initially balls are stationary. But I is given velocity of `10m//s` towards ball II, collision between balls I and II is inelastic with coefficient of restitution `0.5` but collision between balls II and III is perfectly elastic. What is the time interval between two consecutive collisions between ball I and II?

Explanation

Let velocity of Ist ball and Iind ball after collision be `v_(1)` and `v_(2)`
`v_(2) -v_(1) = 0.5 xx 10` ...............(i)
`mv_(2) + m_(1)v_(1) = m xx 10` .......................(ii)
`rArr v_(2) + v_(1) = 10`
Solving Eqs. (i) and (ii)
`v_(1) = 2.5 ms^(-1)`, `v_(2) = 7.5 ms^(-1)`
Ball II after moving 10 m collides with ball III elastically and stops. But ball I moves towards ball II. Time taken between two consecutive collisions.
`(10/7.5) + (10 - 10 xx (2.5)/(7.5))/(2.5) = 4s`