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Q.

A horizontal disc rotates freely about a vertical axis through its centre. A ring, having the same mass and radius as the disc, is now gently placed on the disc. After some time, they rotate with a common angular speed.

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a

some friction exists between the disc and the ring.

b

the angular momentum of the disc plus ring is conserved.

c

the final common angular speed is 23rd of the initial angular velocity of the disc.

d

23rd of the initial kinetic energy changes to heat.

answer is A.

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Detailed Solution

By conservation of angular momentum,I1ωi=I1+I2ωfωf=ω1/3Ei=12I1ωi2Ef=12I1+I2ωf2 Ratio of the heat produced to initial kinetic energy =Ei−EfEi=23

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A horizontal disc rotates freely about a vertical axis through its centre. A ring, having the same mass and radius as the disc, is now gently placed on the disc. After some time, they rotate with a common angular speed.