Velocity of the centre of a small cylinder is `v`. There is no slipping anywhere. The velocity of the centre of the larger cylinder is

Options

A. `2v`
B. `v`
C. `(3v)/2`
D. none of the above

Answer

B

Explanation

In figure `C_(1)` and `C_(2)` are `IC` (instantaneous centre of rotation) of the two cylinders. The cylinder can be considerede as rotation about `C_(1)` and `C_(2)`. In the absence of slipping between the plank and the cylinders, point `A_(1)` and `A_(2)` have the same velocity.
Angular velocity of the larger cylinder is `(2v)/(4R)=v/(2R)`

`v_(CM)=(2R)(v/(2R))=v`