NEET-XII-Physics
10: Rotational Mechanics
- #26A 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 (figure 10-Q4). 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) 4l.
Figure
digAnsr: bAns : (b) 2l
For pure rolling, `` \omega r={v}_{0}``
Figure:
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``
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