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

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

Correct answer: 2k/I θ

Solution

The kinetic energy of the disc is given as kθ², and using the relationship between kinetic energy and angular motion, we can derive that the angular acceleration is proportional to the torque applied, which results in the expression 2k/I θ, indicating that the angular acceleration increases with the angle of rotation.

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