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. $\frac{F}{3 \, m R}$
• B. $\frac{3 F}{2 \, m \, R}$
• C. $\frac{2 F}{3 \, m \, R}$
• D. $\frac{F}{2 \, m \, R}$

Answer 1

Answer: (C)

$F-f_{r}=ma$ $\ldots \left(i\right)$
$f_{r}R=I\alpha =\frac{m R^{2}}{2}\alpha $ $\ldots \left(\right.ii\left.\right)$
For pure rolling
$a=\alpha R$ $\ldots \left(\right.iii\left.\right)$
From $\left(i\right), \, \left(\right.ii\left.\right)$ and $\left(\right.iii\left.\right)$
$F-\frac{m R \, \alpha }{2}=m\alpha R$
$F=\frac{3}{2}mR \, \alpha $
$\alpha =\frac{2 F}{3 m R}$