Question

A thin string is wrapped several times around a cylinder kept on a rough horizontal surface. A boy standing at a distance L from the cylinder draws the string towards him as shown in the figure. The cylinder rolls without slipping. The length of the string passed through the hand of the boy while the cylinder reaches his hand is

• A. L
• B. 2L
• C. 3L
• D. 4L

Answer 1

The correct option is B 2L

Let the angular speed of cylinder be V and linear speed of it COM is V

Then

$Wr=V$

where $r=$radius of cylinder.

Now as the string touches the cylinder the speed of any point of string is

$V+wp=2V$

It in time $t=\frac{L}{V}$ cylinder reaches the boy, the string will cover a distance ${}^{\prime }2Vt=2L^{\prime }$ in the time.