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Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the axis passing through its centre. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 rads2 is


A
78.5 N
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B
157 N
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C
25 N
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D
50 N
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Solution

The correct option is C 25 N
Let, the tension produced in the string be T.
Then, the torque due to the tension T about the centre of the cylinder of radius R is given by,

τ=T×R
where, τ=Iα=12MR2×α
(Since moment of inertia of cylinder about the axis passing through its centre, I=12MR2)
T×R=12MR2×α

T=12MR×α

T=12×50×0.5×2=25 N.


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