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

Options

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

Answer

D

Explanation

Tension in the string is force acting on the cylinder which rotates it. `alpha=2rev//s^(2)=2xx2pirad//s^(2)`
`TR=Ialpha`
`TR=(1)/(2)MR^(2)alpha`
`T=(1)/(2)MRalpha`
`=(1)/(2)xx50xx(0.5)(2xx2pi)`
`=25xx(5)/(10)xx4pi=157.07N`