Q 11-06-201NEETEAMCET 2008 (Medical)Medium
If the Earth shrinks such that its density becomes $8$ times the present value, then the new duration of the day in hours will be
Answer: (C) $6$
The mass stays the same, so $8$ times the density means $\dfrac{1}{8}$ of the volume, i.e. half the radius.
With no external torque, $I\omega$ is constant and $I \propto R^2$, so $\omega$ becomes $4$ times and the day becomes $\dfrac{24}{4} = 6$ hours.
Solution by Sreeraj P, M.Sc Physics