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 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 hand is:

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

Answer 1

Answer: (B)

$2l$

Since this is a case of pure rolling.

velocity at the lowest point will be zero,

And the velocity of the highest point will be twice as that of the center.

so, when center travels a distance "l" topmost point travel an equivalent distance of "2l".

hence,

The length of the string passed through the hand of the man while the cylinder reaches his hand is $2l$

hence option B is correct.