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Question

# A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. 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 revolutions/s2 is

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

## The correct option is D 157 NGiven: A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. To find the tension in the string required to produce an angular acceleration of 2 rev/s2Solution:Here as per the given criteria,m=50kgr=0.5mα=2rev/s2=4πrad/s2For solid cylinder moment of inertia about its central axis isI=12mr2And the torque produced by the tension T in the string will beτ=TrBut we know, τ=IαHence Tr=Iα⟹Tr=12mr2×4π⟹T=2πmrNow substituting the corresponding values we getT=2×227×50×0.5⟹T≈157Nis the tension in the string required to produce an angular acceleration of 2 rev/s2

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