A uniform solid sphere of radius `r` is rolling on a smooth horizontal surface with velocity `v` and angular velocity `omega = (v=omega r)`. The sphere collides with a sharp edge on the wall as shown in figure. The coefficient of friction between the sphere and the edge `mu=1//5`. Just after the collision the angular velocity of the sphere becomes equal to zero. The linear velocity of the surface just after the collision is equal to

Options

A. `v`
B. `v/5`
C. `(3v)/5`
D. `v/6`

Answer

A

Explanation

Impulse provided by the edge in the horizontal direction
`-intNdt =-mV^(1)-(MV)....(1)`
Friction impulse in the vertical direction
`muRintNdt=2/5 mR^(2)(V/R)....(2)`
from eq(1) and (2) we get
`int Ndt=2mV` and `V^(1)=V`