Radius of the cylinder,\( R = 0.5 m\)

Angular acceleration, \(\alpha  = 2\,rev\,{s^{ - 2}}\)

\( = 2 \times 2\pi \,rad\,{s^{ - 2}} = 4\pi \,rad\,{s^{ - 2}}\)

Torque, \(\tau \, = TR\)

Moment of inertia of the solid cylinder about its 

axis, \(I = \frac{1}{2}M{R^2}\)

\(\therefore \) Angular acceleration of the cylinder

                       \(\alpha  = \frac{\tau }{I} = \frac{{TR}}{{\frac{1}{2}\,M{R^2}}}\)

\(T = \frac{{MR\alpha }}{2} = \frac{{50 \times 0.5 \times 4\pi }}{2} = 157\,N\)