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The acceleration a of the plank P required to keep the center C of a solid cylinder in a fixed position during the motion is (no slipping takes place between cylinder and plank)

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$\frac{g}{2}$ sinθ

$2 g \sin θ$

$g \sin θ$

$\sqrt{2} g \sin θ$

answer is B.

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Detailed Solution

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

mg sinθ = frictional force (f) upwards

(here m= mass of cylinder)
∴ Angular acceleration about C is ∝=τ/I,

We know, I=mr²/2, and τ=fR

For no slipping between cylinder and plank,

a =R∝=2g sinθ

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