A uniform solid sphere of radius `r` is rolling on a smooth horizontal surface with velocity `V` and angular velocity `omega(V=omegar)`. The sphere collides with a sharp edge on the wall as shown in Fig. 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 sphere 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'-(mV)`..i
Friction impulse in the vertical direction
`muRintNdt=2/5mr^(2)(V/R)`…….ii
Form eqn i annd ii we get
`intNdt=2mV` and `V'=V`