find the value of g at poles and at equator.

The expression for variation of g with latitude is given as,

g'=g-R_eω²cos²λ     ... (1)

where,

g' is the acceleration due to gravity in presence of Earth's rotation

λ is latitude

g is the acceleration due to gravity

R_e is the radius of the Earth

ω is the angular velocity

 

At the equator:

λ=0, cos λ=cos 0=1

Thus from eqn (1), we get,

g'=g-R_eω²

Substituting R_e=6.37×10⁶ m and , we get,

g-g' = R_eω² = (6.37×10⁶ m) (7.27×10^-5 s^-1)² = 0.034 m s^-2.

We see that g', the acceleration due to gravity at the equator of the rotating Earth, is less than g, the expected value if the Earth were not rotating by only 0.034/9.8 or 0.35%. 

The effect diminishes as we go to higher latitudes at the poles.

 

At the poles:

λ=90°, cos λ=cos 90°=0

Thus, from eqn(1),

g'=g

 

Hence, we conclude that as we go from the equator towards the poles, the value of g goes on increasing.