Question

A homogeneous solid cylindrical roller of radius $R$ and mass $M$ is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

• A. $\frac{2F}{3mR}$
• B. $\frac{3F}{2mR}$
• C. $\frac{F}{3mR}$
• D. $\frac{F}{2mR}$

Answer 1

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

Given:
Roller radius $=R$
Roller mass $=M$
Applying horizontal force balance,
$F-F_r=ma$ ... $\left(i\right)$

Taking moment about central axis of the roller,

$F_r.R=I\alpha =\frac{m{R}^2}{2}\alpha$ ... $\left(ii\right)$

For pure rolling

$a=\alpha .R$ ... $\left(iii\right)$

From $\left(i\right),\left(ii\right)$ and $\left(iii\right)$

$F-\frac{mR\alpha }{2}=m\alpha R$

$F=\frac{3}{2}mR\alpha$

$\alpha =\frac{2F}{3mR}$

Hence, option $\left(D\right)$ is correct.