A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity `v_(0)`. When it finally starts rolling without slipping the speed of its centre is

Options

A. `2/7v_(0)`
B. `3/7v_(0)`
C. `5/7v_(0)`
D. `6/7v_(0)`

Answer

C

Explanation

Let M and R be mass and radius of the solid sphere respectively.
Applying law of conservation of angular momentum about the point of contact, we get
`Mv_(0)R=MvR+2/5MR^(2)omega(because` For solid sphere, `I=2/5MR^(2))`
`=MvR+2/5MR^(2)(v/R)=7/5MvR(becausev=Romega)`
`v_(0)=7/5v` or `v=5/7v_(0)`