A solid cylinder of mass $$2$$ kg and radius $$4$$ cm is rotating about its axis at the rate of $$3$$ rpm. The torque required to stop after $$2$$π revolutions is [NEET $$2019$$]

Question

A solid cylinder of mass $$2$$ kg and radius $$4$$ cm is rotating about its axis at the rate of $$3$$ rpm. The torque required to stop after $$2$$π revolutions is [NEET $$2019$$]

Infinity Learn · Accepted Answer

Given, mass of cylinder,  $$m=2$$ kgRadius of cylinder,  $$r=4$$ $$cm=4$$×$$10-2$$ mRotational velocity,  $$3rpm=3$$×$$2$$$$π$$$$60=$$π$$10rads-1$$ and θ$$=2$$π× revolution $$=2$$π×$$2$$π$$=4$$$$π$$$$2radThe$$ work done in rotating an object by an angle  θ from rest is given by  $$W=$$τθAs the cylinder is brought to rest, so the work done will be negative.According to $$work-energy$$ theorem,Work done $$=$$ Change in rotational kinetic $$energy-$$τθ$$=12I$$ω$$f2-12I$$ω$$i2=12I$$ω$$f2-$$ω$$i2$$⇒  τ$$=I$$ω$$i22$$θ   ∵ω$$f-0=1212mr2$$ω$$i2$$θ  ∵$$I=12mr2($$ for cylinder $$)=14mr2$$ω$$2$$θ  ∵ω$$i=$$ω$$=14$$×$$2$$×$$4$$×$$10-22$$×π$$102$$×$$14$$$$π$$$$2=14$$×$$2$$×$$16$$×$$10-4$$×π$$2100$$×$$14$$$$π$$$$2=2100$$×$$10-4=2$$×$$10-6$$ $$N-m$$

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 $π$ revolutions is [NEET 2019]

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A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is [NEET 2019]

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A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 $π$ revolutions is [NEET 2019]