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) $2\pi\sqrt{\dfrac{2R}{g}}$
Concept. At the equator $g' = g - \omega^2R$.
Step 1. Condition. $g' = \dfrac g2 \Rightarrow \omega^2R = \dfrac g2$.
Step 2. Period. $T = \dfrac{2\pi}{\omega} = 2\pi\sqrt{\dfrac{2R}{g}}$.
Answer. $2\pi\sqrt{\dfrac{2R}{g}}$ (Option A).
Solution by Sreeraj P, M.Sc Physics