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
$I{\omega }_0=\left(m{\upsilon }_0\right)h$
$\left(\frac{2}{5}m{r}^2\right){\omega }_0=\left(m{\upsilon }_0\right)h$
$\therefore {\omega }_0=\frac{5{\upsilon }_{0}h}{2r^2}$