Question

An unstretchable massless rope is wrapped around a solid cylinder of mass $m$ and radius $r$. One end of the rope is fixed while cylinder is released from the rest. The acceleration of the centre of cylinder is

• A. $\frac{2}{3}g$
• B. $\frac{1}{2}g$
• C. $\frac{3}{2}g$
• D. $\frac{3}{4}g$

Answer 1

The correct option is A $\frac{2}{3}g$

We know that the acceleration for such a case is
$a=-\frac{g}{1+\frac{I}{m{r}^2}}$(negative sign indicates the opposite direction)
for a solid cylinder we have $I=\frac{1}{2}m{r}^2$
Thus we get
$a=\frac{2}{3}g$