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 `theta`, where `theta` is the angle by which it has rotated, is given as `k theta`. If its moment of inertia is I then the angular acceleration of the disc is :

Options

A. `k/(2I)theta`
B. `k/I theta`
C. `k/(4I) theta`
D. `(2k)/I theta`

Answer

D

Explanation

`1/2 Iomega^(2) = K theta^(2) rArr 1/2 I xx cancel(omega) xx (domega)(dt) = K xx 2theta.cancel((d theta)(dt))`, therefore `alpha =(domega)/(dt) = (2k theta)/I`