If 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 earth) (Ignore equatorial bulge)

Options

A. `2pi sqrt((2R)/g)`
B. `2pi sqrt(R/(2g))`
C. `2pisqrt(R/(3g))`
D. `2pisqrt(R/g)`

Answer

A

Explanation

`g_(phi)=g-Romega^(2)cos^(2)phi`