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A string is wrapped around a cylinder of...

A string is wrapped around a cylinder of mass `M` and radius `R`. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string. The tension in the string is

A

`(Mg)/6`

B

`(Mg)/3`

C

`(Mg)/2`

D

`(2Mg)/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of motion
`Mg-T=Ma` ………….i
Taking torque about the axis passing through the centre of the spool and perpendicular to it
`TR=Ialpha=1/2MR^(2)(a/2)`
`T=1/2Ma` …………ii
From eqn i and ii
`Ma=Mg-1/2ma`
`a=(2g)/3`
`:. T=(Mg)/3`
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