Q 11-07-023NEETEAMCET 2013 (Medical)Medium
If the earth were to rotate on its own axis such that the weight of a person at the equator becomes half the weight at the poles, then its time period of rotation is ($g$ = acceleration due to gravity near the poles and $R$ is the radius of the earth; ignore equatorial bulge)
Answer: (A) $2\pi\sqrt{\dfrac{2R}{g}}$
At the equator $g' = g - \omega^2R$. Setting $g' = \dfrac{g}{2}$:
$$\omega^2R = \frac{g}{2} \;\Rightarrow\; \omega = \sqrt{\frac{g}{2R}} \;\Rightarrow\; T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{2R}{g}}$$
Solution by Sreeraj P, M.Sc Physics