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 $$s-2is$$

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  $$s-2is$$

Infinity Learn · Accepted Answer

Here, mass of the cylinder, M $$=$$ $$50$$ kg Radius of the cylinder, R $$=$$ $$0.5$$ m Angular acceleration, α$$=2$$ rev s−$$2=2$$×$$2$$$$π$$rad⁡s−$$2=4$$$$π$$rads−$$2$$ Torque, τ$$=TRMoment$$ of inertia of the solid cylinder about its axis,$$I=12MR2$$∴  Angular acceleration of the cylinder α$$=$$τ$$I=TR12MR2T=MR$$α$$2=50$$×$$0.5$$×$$4$$$$π$$$$2=157N$$

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