Question

The figure shows a fixed incline plane on which a plank is being pulled upwards such that the centre $C$ of the solid cylinder remains at rest with respect to ground. If no slipping takes place between the cylinder and the plank, then the acceleration of the plank is

• A. $\frac{\text{g}}{2} \text{sin} \theta $
• B. $2 \text{g} \text{sin} \theta $
• C. $\text{g} \text{sin} \theta $
• D. $\sqrt{2} \text{g} \text{sin} \theta $

Answer 1

Answer: (B)

Linear acceleration of cylinder is zero, i.e.,
$mg \, sin \, \theta =f$ ( here $f$ = frictional force upwards )
Angular acceleration about the centre $\alpha =\frac{\tau}{I}$
or $\alpha =\frac{\text{fR}}{\frac{1}{2} \text{mR}^{2}}=\frac{\text{2f}}{\text{mR}}$
or $\alpha =\frac{\text{2mg sin} \theta }{\text{mR}}=\frac{\text{2g sin} \theta }{\text{R}}$
For no slipping between cylinder and plank
$a=\text{R}\alpha =\text{2g sin}\theta $