A cylinder of mass `50 mg` 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. Tension in the string required to produce an angular acceleration of `2` revolutions `s^-2` is

Options

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

Answer

D

Explanation

(d) Applying torque equation about center of cylinder
`tau = I prop`
`prop` is the angular acceleration of cylinder and it is given
`prop = 2 revolution//s^2 = 2 xx 2 pi = 4 pi rad//s^2`
`T r = I prop`
`T = (I prop)/(r) = (mr^2)/(2) xx (prop)/(r) = (mr prop)/(2)`
=`(50 xx 0.5 xx 4 pi)/(2) N = 157 N`.
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