A solid sphere of mass `M` and radius `R` is placed on a rough horizontal surface. It is stuck by a horizontal cue stick at a height `h` above the surface. The value of `h` so that the sphere performs pure rolling motion immediately after it has been stuck is

Options

A. `(2R)/5`
B. `(5R)/2`
C. `(7R)/5`
D. `(9R)/5`

Answer

C

Explanation

Let `v` be the velocity of the centre of mass of the sphere and `omega` be the angular velocity of the body about an axis passing through the centre of mass.
`J=Mv`
`J(h-R)=2/5MR^(2)xxomega`
From the above two equations `=v(h-R)=2/5r^(2)omega`
From the condition of pure rolling `v=Romega`
`h-R=(2R)/5impliesh=(7R)/5`