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A billiard ball of mass m and radius r, ...

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

A

`(2v_(0)h)/(5r^(2))`

B

`(5v_(0)h)/(2r^(2))`

C

`(2v_(0)r^(2))/(5h)`

D

`(5v_(0)r^(2))/(2h)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let J be the linear impulse imparted to the ball. Applying impulse = change in momentum we have
`J=mv_(0)`………….(i)
`Jh = Iomega_(0) = 2/5 m r^(2) omega_(0)`……….(2)
From Eqs. (1) and (2) we get: `omega_(0) = 5/2.(v_(0)h)/(r^(2))`
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