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A solid cylinder of mass 50 kg and radiu...

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. What is the tension in the string required to produce an angular acceleration of 2 revolutions `s^(-2)` ?

Text Solution

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Here, mass of the cylinder, M = 50 kg
Radius of the cylinder, R = 0.5 m
Angular acceleration, `alpha=2 "rev s"^(-2) = 2xx 2 pi"rad s"^(-2)=4pi "rad s"^(-20`
Torque, `tau=TR `

Moment of inertia of the solid cylinder about its axis `I=(1)/2 MR^2`
Angular acceleration of the cylinder `alpha=tau/I=(TR)/(1/2MR^2)`
`T = (MRalpha)/2=(50xx0.5xx4pi)/2=157N`
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