Question

A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque τ on the disc and it stops after making 5 revolutions, then in how many revolutions will the ring stop under the same retarding torque?

Answer 1

A ring and a disc of different masses are rotating with the same kinetic energy.

so, kinetic energy of ring = kinetic energy of disc

or, $\frac{1}{2}I_1\omega_1^2=\frac{1}{2}I_2\omega_2^2$....(1)

if we apply a retarding torque τ on the disc and it stops after making 5 revolutions.

workdone due to torque in case of disc = kinetic energy of disc

or, $\tau.\theta_2=\frac{1}{2}I_2\omega_2^2$

or, $\tau.2\pi 5=\frac{1}{2}I_2\omega_2^2$......(2)

similarly, workdone due to torque in case of ring = kinetic energy of ring.

or, $\tau.\theta_1=\frac{1}{2}I_1\omega_1^2$

from equations (1) and (2),

$\tau.2\pi n_1=\tau 2\pi 5$

so, $n_1=5$

hence, number of revolution with the ring = 5