Question

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`

Answer 1

Correct Answer - 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`