question_answer

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- [JEE Main Online Paper (Held On 10-Jan-2019 Morning]

A) \[\frac{F}{2mR}\]                              

B) \[\frac{2\,F}{3mR}\]

C) \[\frac{3\,F}{2mR}\]              

D)   \[\frac{F}{3mR}\]

Correct Answer: B

Solution :

\[{{_{\tau abt}}_{A\,}}\,=\,\,{{I}_{A\alpha }}\] \[F\times R=\left( \frac{1}{2}M{{R}^{2}}+M{{R}^{2}} \right)\alpha \] \[\alpha \,\,=\,\,\frac{2F}{3mR}\] Note: In this question value of force and its point of application is not given so its answer cannot be given. We are giving its answer by assuming that F is applied at centre of cylinder.