A billiard ball of mass m and radius 7, 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 Wo acquired by the ball is

Options

A. `(5v_(0) r^(2))/(2h)`
B. `(2 v_(0) r^(2))/(5h)`
C. `(2 v_(0) h)/(5r^(2))`
D. `(5 v_(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)`
As is clear from figure

Angular momentum = Moment of momentum
`I omega_(0) = (mv_(0) ) h or (2)/(5) mr^(2) omega_(0) = mv_(0) h or omega_(0) = (5 v_(0) h)/(2r^(2))`