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_o . The angular velocity $ω_{o}$ acquired by the ball is

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$\frac{5 v_{0} h}{2 r^{2}}$

$\frac{5 v_{0} r^{2}}{2 h}$

$\frac{2 v_{0} h}{5 r^{2}}$

$\frac{2 v_{0} r^{2}}{5 h}$

answer is D.

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Detailed Solution

$Impulse = Δp = {mv}_{0}$

About centre of mass
$L = {Iω}_{0} = ({mv}_{0}) h$
$\Rightarrow \frac{2}{5} {mr}^{2} ω_{0} = {mv}_{0} h \Rightarrow ω_{0} = \frac{5 v_{0} h}{2 r^{2}}$

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