Question

A cylindrical drum, pushed along by a board rolls forward on the ground. There is on slipping at any contact. Find the distance moved by the man who is pushing the board, when axis of the cylinder covers a distance L.

• A. 2L
• B. L
• C. Lω
• D. None of these

Answer 1

The correct option is A

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 hence $\omega =\frac{v_0}{R}$ Where R is the radius of the cylinder

Speed of the topmost point is $v=v_0+\omega R=2v_0$

Since 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 = $2v_0\times \frac{L}{v_0}=2L$

As there is no slipping between any points of contact hence distance moved by the man is 2L.