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

Question

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 hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $\mathrm{s}^{-2}$ is\

Professor PC Thomas Classes · Answer

(d) : Here, mass of the cylinder, $M=50 \mathrm{~kg}$ Radius of the cylinder, $R=0.5 \mathrm{~m}$\ Angular acceleration, $\alpha=2 \mathrm{rev} \mathrm{s}^{-2}$\ $=2 	imes 2 \pi \mathrm{rad} \mathrm{s}^{-2}=4 \pi \mathrm{rad} \mathrm{s}^{-2}$\ Torque, $	au=T R$\ Moment of inertia of the solid\ cylinder about its axis, $I=\frac{1}{2} M R^{2}$\ $	herefore$ Angular acceleration of the cylinder, $\alpha=\frac{	au}{I}=\frac{T R}{\frac{1}{2} M R^{2}}$\ $M R \alpha \quad 50 	imes 0.5 	imes 4 \pi$ $$ T=\frac{M R \alpha}{2}=\frac{50 	imes 0.5 	imes 4 \pi}{2}=157 \mathrm{~N} $$