A solid sphere is rolling without slipping on rough ground as shown in figure. If collides elastically with an identical another sphere at rest. There is no friction between the two spheres . Radius of each sphere is R and mass is m.

Linear velocity of first sphere after it again starts rolling without slipping is

Options

A. `2/5 omega R`
B. `2/7 omega R`
C. `7/10 omega R`
D. `7/5 omega R`

Answer

B

Explanation

Just after collision it will have only i.e., it will slip backwards. So, friction will be maximum and in forward direction. Let `v^(')` be its linear speed and its angular speed when it again starts pure rolling. Friction is passing through its bottommost point, so we can conserve angular momentum about an axis passing through its bottommost point and perpendicular to plane of motion
`L_(i) = L_(f)`
`2/5mR^(2)omega = 2/5 (mR^(2)) omega^(') + mR v^(')`

`omega' =v^(')/R therefore v^(') = 2/7 omega R`