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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 end hanging freely. Tension in the string required to produce an angular acceleration of `2` revolution `s^(-2)` is

Text Solution

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`Mg-T=Ma.....(1)` Also, `tau =TR=Ialpha`
`rArrT=(Ialpha)/R=(MR alpha)/2......(2)`
Where `I=1/2MR^(2)`
Condition for no slipping, `a=alphaR...(3)`
Solving equations (1), (2) and (3) we obtain
`a=2/3g` and `T=(Mg)/3`
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