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

157 N

\(\alpha\) = 2 revolution/ s² = 4\(\pi\)/s²

I = \(\frac{1}{2}\)MR²

As \(\tau\) = I\(\alpha\) so TR= I\(\alpha\)

TR= \(\frac{MR^2}{2}\)\(\alpha\)

T= \(\frac{MR}{2}\)\(\alpha\)

⇒ T =\(\frac{I\alpha}{R}\) = \(\frac{50 × 0.5 × (4\pi)}{2}\)N

       = 50\(\pi\)N =  157N