Question 265 of 280

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$\dfrac{F}{3mR}$B$\dfrac{3F}{2mR}$C$\dfrac{2F}{3mR}$D$\dfrac{F}{2mR}$

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Answer: (C) $\dfrac{2F}{3mR}$

$F-{f}_{r}=ma$ $\ldots \left(i\right)$

${f}_{r}R=I\alpha =\dfrac{m{R}^{2}}{2}\alpha$ $\ldots (ii)$

For pure rolling

$a=\alpha R$ $\ldots (iii)$

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

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

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

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