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A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ². If its moment of inertia is I, then the angular acceleration of the disc is -

1. k/I θ
2. k/2I θ
3. k/4I θ
4. 2k/I θ

Correct answer: 2k/I θ

Solution

KE = k*theta^2, so torque = d(KE)/d(theta) = 2k*theta = I*alpha. Hence angular acceleration alpha = 2k*theta/I.

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