A cylinder of mass M and radius .H is resting on a horizontal platform which is parallel to $$X-Y$$ $$plane)$$ with its axis fixed along the $$Y-axis$$ and free to rotate about its axis. The platform is given a motion in $$X-direction$$ given by x $$=$$ A $$cos$$ ωt. There is no slipping between the cylinder and platform. The maximum torque acting on the cyliner during its motion is

Question

A cylinder of mass M and radius .H is resting on a horizontal platform which is parallel to $$X-Y$$ $$plane)$$ with its axis fixed along the $$Y-axis$$ and free to rotate about its axis. The platform is given a motion in $$X-direction$$ given by x $$=$$ A $$cos$$ ωt. There is no slipping between the cylinder and platform. The maximum torque acting on the cyliner during its motion is

Infinity Learn · Accepted Answer

τ$$=I$$α$$=12MR2$$×$$($$ acceleration $$/R)acceleration$$ $$=$$−ω$$2Asin$$⁡ωt  or   (acc$$.$$) $$max=$$ω$$2A$$∴ $$($$τ$$)max=12MR2$$ω$$2A/R=12MRA$$ω$$2$$

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