Eddy current brakes are brakes that use eddy currents generated by electromagnetic induction to slow down an object. Eddy current brakes are widely used in high speed trains and roller coasters. Since there is no physical contact, eddy current brakes are much quieter and last much longer before wearing down as compared to frictional brakes.

The diagram above shows the working of a circular eddy current brake. To slow down the rotating disk, the electromagnet is switched on. This causes circular loops of currents, called eddy currents, to be formed in the disk. Since the disk has resistance, and current flows through it, heat is generated and the kinetic energy of the disk decreases.

Initially, the disk D has rotates with angular velocity $\omega$. After the brakes are applied for some time, the angular velocity of the disk becomes $\omega /10$.

Find $\dfrac{K_{\text{final}}}{K_{\text{initial}}}$, the ratio of final rotational kinetic energy to the initial rotational kinetic energy of the disk.

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