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?

Answer

D

Explanation

Let velocity of I ball and II ball after collision be `v_1` and `v_2`
`v_2-v_1=0.5xx10` …(i)
`mv_2+mv_1=mxx10` …(ii)
`impliesv_2+v_1=10`
Solving Eqs. (i) and (ii), we get `v_1=2.5m//s`, `v_2=7.5m//s`
Ball II after moving `10m` collides with ball III elastically and stops. But ball I moves towards ball II. Time taken between two consecutive collisions
`10/7.5-(10-10xx2.5/7.5)/(2.5)=4s`