Question

A small block of mass ‘m’ is rigidly attached at ‘P to a ring of mass ‘3m’ and radius ‘r’. The system is released from rest at $\theta ={90}^{\circ }$ and rolls without sliding. The angular acceleration of hoop about the center of the ring, just after release is

• A. $\frac{g}{4r}$
• B. $\frac{g}{8r}$
• C. $\frac{g}{3r}$
• D. $\frac{g}{2r}$

Answer 1

The correct option is B $\frac{g}{8r}$

f = 4 ma ....... (1)

$(mg-f)r=(3m{r}^2+m{r}^2)a$



mg - f = 4 ma ...... (2)

From (1) and (2) 8 ma = mg $a=\frac{g}{8}$ $a=\frac{g}{8r}$