Question

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

Answer 1

Correct option is (b) 2g sinθ

Let the angular acceleration be a 

torque equation

mgr = I x α

Where I = moment of inertia 

\(mg \,sin\,θ \,r = \frac{mr^2}{2}\times \alpha\)

\(\alpha=\frac{2g\,sin\,\theta}{\pi}\)

for pure rolling a = α r

a \(=\frac{2g\,sin\,\theta}{r}.r\)

a = 2g sinθ