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Question

A solid cylinder of mass 50kg and radius 0.5m is free to rotate about the horizontal axis. A massless string is wound end round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2rev/s2

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

The correct option is A 157NMass, m=50kgRadius, r=0.5m,Angular acceleration α=2rev/s2=4π red/s2Torque produces by the tension a string=T×R=T×0.5=T/2 N/m ....(1)we know,T=Iα ........(2)From equation (1) & (2)T2=Iα=(MR22)×(4π)rads2∴ Tsolidcylinder=MR22I2=50×0.522×4πT=50πT=157N.

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