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. `e + 1)/(e-1)`
D. `(e-1)/(e+1)`

Answer

B

Explanation

From conservation of linear momentum:

From definition of e,
`v_(1) - v_(2) = eu`..............(ii)
Solving these two equations, we get
`v_(1) = (1+e)/(2)u` and `v_(2) = (1-e)/(2)u`
`therefore` `(v_(1)/(v_(2) = (1+e)/(1-e)`