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 (shown in the figure). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hand is:

A. $L$
B. $2L$
C. $3L$
D. $4L$

Answer 1

Hint: The top of the cylinder is circular. Its length is given by the circumference of this circle having some radius. Whenever two surfaces move relative to each other, force starts acting on them which opposes their relative motion. This force is called the force of friction.

Complete step by step solution:
According to the question, the man is at a distance of L from the cylinder. It means the length of the string is unwrapped. Now, the cylinder has to cover the L distance to reach his hands. This means another length L of the string has to be unwrapped. Therefore, the total 2L length of the string has to be unwrapped from the cylinder. This length L will be multiple of the circumference of the circular top, that is, $2\pi (radius)$.
Therefore, 2L is the length of the string passed through the hand of the man while the cylinder reaches his hands.s
Hence, the correct option is (B) $2L$.

Note:
When surfaces are smooth, then the object starts slipping. That is when there is a lack of friction slipping happens.
Friction force always acts in the direction opposite to the net force.