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 (see the following figure). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is _________ .
Options
`l`
`2l`
`3l`
`4l`
Solution
`2l`
For pure rolling,
\[\omega r = v_0\]
As shown in the figure, the velocity of the string will be resultant of v0 and ωr.
\[v_{net} = v_0 + \left( \omega r \right)\]
\[ v_{net} = 2 v_0\]
Let,
Linear distance travelled by the cylinder in time (t),
\[v_0 t = l\]
∴ Linear distance travelled by the string in same time,
\[2 v_0 t = 2l\]
Notes
Missing Figures
