Question

A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance $l$ from the cylinder holds one end of the string and pulls the cylinder towards him (fig). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is

• A. $l$
• B. $2l$
• C. $3l$
• D. $4l$

Answer 1

The correct option is B $2l$

Suppose radius is $r$

When cylinder moves a distance L it swepts a angle $\frac{L}{r}$

So extra string unwound$=\frac{L}{r}=L$

So total string pulled is $L+L=2L$