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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

A

78.5 N

B

157 N

C

25 N

D

50 N

Text Solution

Verified by Experts

The correct Answer is:
C
`"The M.I. of solid cylinder about its axis is I"=(MR^(2))/(2)`
When the rope is pulled by a force (F), a torque `tau=FxxR`
is producd and it produces the angular acceleration `(alpha)`.
`therefore" "alpha=(tau)/(I)=(FxxR)/(I)" but F = Tension (T) in the string"`
`therefore" "alpha=(TxxR)/((MR^(2))/(2))=(2T)/(MR)`
`therefore T=(MRalpha)/(2)=(50xx0.5xx2)/(2)=25N`
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