A cylindrical drum, pushed along by a board rolls forward on the ground. There is no slipping at any contact. The distance moved by the man who is pushing the board, when axis of the cylinder covers a distance `L` will be.

Options

A. `L`
B. `2 L'
C. `pi L`
D. `8 pi L`

Answer

B

Explanation

(b) Let `v_o` be the linear speed of the axis of the cylinder and `omega` be its angular speed about the axis. As it does not slip on the ground hence `omega = (v_o)/(R )`. Where `R` is the radius of the cylinder.
Speed of the topmost point is `v = v_o + omega R = 2 v_o`
Since time taken by the axis to move a distance `L` is equal to `t = L//v_o`
In the same interval of time distance moved by the topmost point is.
`S = 2 v_o xx (L)/(v_o) = 2 L`.