A small ball rolls off the top landing of a staircase. It strikes the mid point of the first step and then mid point of the second step. The steps are smooth & identical in height & width. The coefficient of restitution between the ball & the first step is :

Options

A. 1
B. `3/4`
C. `1/2`
D. `1/4`

Answer

B

Explanation

C to D `v_(2) = sqrt(2gx) = gt` `therefore = (v_(2))/(g)`
From A to B, time willl become two times.
Applying `S = ut+1/2at^(2)` in vertical direction, we have
`-x = (ev_(2)(2t) -1/2xx g xx(2t)^(2)`
`-x = (2ev_(2)^(2))/(g) - (2v_(2)^(2)) rArr -x = 2e(2x)-2(2x)`
`therefore e=3/4`