Question

A cylindrical drum, pushed along by a board roll 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

• A. $\pi L$
• B. $8\pi L$
• C. $L$
• D. $2L$

Answer 1

The correct option is D $2L$

let $v_0$ 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,$\omega =\frac{v_0}{R}$
Here $R$ is the radius of cylinder
Speed at topmost point is $v=v_0+\omega R$
$v=2v_0$
Time taken by the axis to move a distance $L$ is equal to
$t=\frac{L}{v_0}$
In the same interval of time distance moved by the topmost point is
$S=2v_0\times \frac{L}{v_0}=2L$
$S=2L$
As there is no slipping between any point of contact,
Distance moved by my man is $2L$

Final answer:(b)