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 around 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

Here , mass of the cylinder , M = 50 kg
Radius of the cylinder , R = 0.5 m
Angular acceleration , `alpha = 2 rev s^(-2)`
`= 2 xx 2pi rad s^(-2) = 4pi rad s^(-2)`
Torque , `tau = TR`
Moment of inertia of the solid cylinder about its axis ,
`I = (1)/(2) MR^(2)`
`therefore` Angular acceleration of the cylinder , `alpha = (tau)/(I) = (TR)/((1)/(2) MR^(2))`
`T = (MR alpha)/(2) = (50 xx 0.5 xx 4pi)/(2) = 157 N`