Question

A particle of mass ${}^{\prime }{m}^{\prime }$ is rigidly attached at ${}^{\prime }{A}^{\prime }$ to a ring of mass ${}^{\prime }3m^{\prime }$ and radius ${}^{\prime }r{.}^{\prime }$ The system is released from rest and rolls without sliding. The angular acceleration of ring just after release is

• A. $\frac{g}{4r}$
• B. $\frac{g}{6r}$
• C. $\frac{g}{8r}$
• D. $\frac{g}{2r}$

Answer 1

The correct option is

B

$\frac{g}{6r}$

Moment of intertial of the system is

$I=3m{r}^2+m{r}^2=4m{r}^2$

Using $\tau =I\alpha =4m{r}^2\alpha$ ...(i)

Torque by force due to the weight of the mass m about point $O$ is

$\tau =mgr$ ...(ii)

Comparing (i) and (ii) we have,

$4m{r}^2\alpha =mgr$

$\alpha =\frac{g}{4r}$