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. 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. none of these

Answer 1

The correct option is B $2l$

as there is no slipping

$v=r\omega v_a=v+r\omega =v+v=2v$

thus velocity of A is twice as of center of cylinder

thus A moves twice distance as of culinder

therefore length of string passing through mans hand is 2l