A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquired a linear velocity `v_(0)`. The angular velocity `omega_(0)` acquired by the ball is

Options

A. `(5v_(0)r^(2))/(2h)`
B. `(2v_(0)r^(2))/(5h)`
C. `(2v_(0)h)/(5r^(2))`
D. `(5v_(0)h)/(2r^(2))`

Answer

D

Explanation

The effect of force F lies at high h.
Torque `tau=Ialpha`
`F.h=(2)/(5)mr^(2).(omega)/(t)[because alpha=(omega)/(t)]`
`m.ah=(2)/(5)mr^(2)(omega)/(t)`
`m.(v_(0))/(t)h=(2)/(5)mr^(2)(omega)/(t)`
`omega=(5v_(0)h)/(2r^(2))`