Question

A hoop of radius $r$ and mass $m$ rotating with an angular velocity ${\omega }_o$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

• A. $\frac{r{\omega }_0}{3}$
• B. $\frac{r{\omega }_0}{2}$
• C. $r{\omega }_0$
• D. $\frac{r{\omega }_0}{4}$

Answer 1

The correct option is B $\frac{r{\omega }_0}{2}$

From conservation of angular momentum
$m{r}^2{\omega }_0=mvr+m{r}^2\frac{v}{r}$.
or
$m{r}^2{\omega }_0=2mvr$
or
$\therefore v=\frac{r{\omega }_0}{2}$