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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$\frac{g}{2} sinθ$

$\sqrt{2 g} sinθ$

$2 gsinθ$

$gsinθ$

answer is B.

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Detailed Solution

Linear acceleration of cylinder is zero, i.e.,
$Mgsin θ = f$ (here f=frictional force upwards)
Angular acceleration about the centre $α = \frac{τ}{I}$
Or $α = \frac{fR}{\frac{1}{2} {mR}^{2}} = \frac{2 f}{mR}$
Or $α = \frac{2 mgsin θ}{mR} = \frac{2 gsin θ}{R}$
For no slipping between cylinder and plank
$a = Rα = 2 gsin θ$