A ring and a disc of different masses are rotating with the same kinetic energy. If a retarding torque `(tau)` is applied to the ring, the ring stops after completing n rotations. If the same retarding torque is applied to the disc, how many rotations would it complete before coming to rest?

Options

A. 2n
B. 4n
C. `(n)/(2)`
D. n

Answer

D

Explanation

The M.I. of the disc and the ring are different. But they have the same kinetic energy (K) and the same retarding torque `(tau)` is applied to both of them.
Using work energy theorem for rotational motion, of the ring we get,
Initial rotational K.E. = Work done before coming to rest
`tau. theta = tau.2pin" ...(1)"`
`[because theta=2pi" in one rotation")`
Similarly for the disc, Initial K.E. `=tau.2pi n'" ...(2)"`
`therefore" From (1) and (2)"`
`tau.2pin'=tau.2pin " "therefore n'=n`