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. The cylinder rolls without slipping . The length of the string passed through the hand of the boy while the cylinder reaches his hand is

Answer 1

As shown in the figure, the velocity of the string will be resultant of v0 and ωr.

vnet=v0+(ωr)vnet=2v0

Let:

Linear distance travelled by the cylinder in time (t), v0t=l

∴ Linear distance travelled by the string in same time, 2v0t=2l