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# 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  ${s}^{-2}$is

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a
25 N
b
50 N
c
78.5 N
d
157 N

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detailed solution

Correct option is D

Here, mass of the cylinder, M = 50 kg Radius of the cylinder, R = 0.5 m Angular acceleration, α=2 rev s−2=2×2πrad⁡s−2=4πrads−2 Torque, τ=TRMoment of inertia of the solid cylinder about its axis,I=12MR2∴  Angular acceleration of the cylinder α=τI=TR12MR2T=MRα2=50×0.5×4π2=157N

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