A sphere of mass m moving with a velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, what is the ratio of the velocities of two spheres after the collision?

Options

A. 1
B. e
C. `(1+e)/(1-e)`
D. `(2-e)/(1+e)`

Answer

C

Explanation

Here `u_1=u,u_2=0`
`therefore e=(v_2-v_1)/(u_2-u_1)=(v_2-v_1)/(u-0)` or `v_2-v_1=eu` ….(i)
By the law of conservation of momentum ,
`m u+m x 0 = mv_1 + mv_2` or `v_1+v_2=u` ….(ii)
Adding (i) and (ii),
`2v_2=u+eu=u(1+e)` or `v_2=(u(1+e))/2`
Again , from (ii),
`v_1=u-v_2=u- (u(1+e))/2 = (u(1-e))/2`
Hence , `v_2/v_1=(1+e)/(1-e)`