A horizontal disc rotates freely about a vertical axis through it centre. A ring, having the same mass and radius as the disc, is now gently placed on the disc. After some time, the two rotate with a common angular velocity. Select the correct statements from the following.

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Infinity Learn · Accepted Answer

Let ω$$1$$ $$=$$ the initial angular velocity of the disc. ω$$2$$ $$=$$ the final common angular velocity of the disc and the ring. For the disc, $$I1=12mr2For$$ the ring, $$l2=mr2By$$ conservation of angular momentum, $$L=I1$$ω$$1$$−$$I1+I2$$ω$$2$$ or  ω$$2=l1$$ω$$1I1+I2=$$ω$$1/3$$ Initial kinetic energy $$=E1=12I1$$ω$$12$$ Final kinetic energy $$=E2=12I1+I2$$ω$$22$$ Heat produced $$=$$ loss in kinetic energy $$=E1$$−$$E2$$ Ratio of heat produced to initial kinetic energy $$=E1$$−$$E2E1=23$$

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