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

When the ball is hit by a cue, the linear impulse imparted to the ball = change in momentum = `mv_(0)`
Angular momentum = Moment of momentum
`Iomega_(0)=(mv_(0))h`
`(2)/(5)mr^(2)omega_(0)=mv_(0)horomega_(0)=(5v_(0)h)/(2r^(2))`