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Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about 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 N
ICylinder=MR22
=50×(12)22
=50×12×4=508 kgm2
Torque due to tension =TR
z=Iα
TR=(508)×2
T×12=504
T=25 N
α=2rev52=2×(2π)52 rad
1 revolution =2π rad.
α=4π rad/s2
z=Iα
T×(12)=(505)×4π=50×π=157.07 N
T=157 N

290501_312788_ans.png

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