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

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Linear acceleration of cylinder is zero, i.e.,

$mg \sin θ = f$ ( here $f$ = frictional force upwards )

Angular acceleration about the centre $α = \frac{τ}{I}$

or $α = \frac{fR}{\frac{1}{2} {mR}^{2}} = \frac{2f}{mR}$

or $α = \frac{2mg sin θ}{mR} = \frac{2g sin θ}{R}$

For no slipping between cylinder and plank

$a = R α = 2g sin θ$

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