A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is would 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

Explanation

Here, `alpha = 2 "rev"cdot s^(-2) = 4 pi " ""rad" cdot s^(-2)`
`I = (1)/(2)MR^(2) = (1)/(2)(50)(0.5) = (25)/(4) kg cdot m^(2)`
As, `tau = I alpha , os, " "TR = I alpha`
`therefore " "T = (I alpha)/(R ) = (((25)/(4)) (4pi))/(0.5) = 50 pi = 157 ` N
The option D is correct.