Question

A billiard ball is hit by a cue at a height h above the centre. It acquires a linear velocity $\upsilon_{0}$. Mass of the ball is m and radius is $r$. The angular velocity $\omega_{0}$ acquired by the ball is

• A. $\frac{2\upsilon_{0}h}{5r^{2}}$
• B. $\frac{5\upsilon_{0}h}{2r^{2}}$
• C. $\frac{2\upsilon_{0}r^2}{5h}$
• D. $\frac{5\upsilon_{0}r^2}{2h}$

Answer 1

Answer: (B)

When the ball is hit by a cue, the linear impulse imparted to the ball = change in momentum $=m\upsilon_{0}$.

As is clear from figure,
Angular momentum = moment of momentum
$I\omega_{0}=\left(m\upsilon_{0}\right)h$
$\left(\frac{2}{5}mr^{2}\right)\omega_{0}=\left(m\upsilon_{0}\right)h$
$\therefore \omega_{0}=\frac{5\upsilon_{0}h}{2r^{2}}$