Sphere A of mass 'm' moving with a constant velocity u hits another stationary sphere B of the same mass. If e is the co-efficient of restitution, then ratio of velocities of the two spheres `v_(A):v_(B)` after collision will be :

Options

A. `((1-e)/(1+e))`
B. `((1+e)/(1-e))`
C. 1
D. none of these

Explanation

Using formula, `v_(1)=(m_(1)-em_(2))/(m_(1)+m_(2))` and `v_(2)=(em_(1)(1+e))/(m_(1)+m_(2))`
`rArr (v_(1))/(v_(2))=(m_(1)-em_(2))/(m_(1)(1+e))`
By putting `m_(1)=m_(2)=m` we obtain `(v_(1))/(v_(2))=(1-e)/(1+e)`