Explain the change in the value of g due to shape of the Earth. - Vidyadip

Question

Explain the change in the value of $g$ due to shape of the Earth.

✓

Answer

Till now we have considered the Earth to be spherical but in reality the Earth is flat at the poles, that is the equatorial radius $\left(R_C\right)$ of the Earth is more and polar radius ( $R_p$ ) is less.

$g=\frac{GM}{r^2} \ \ldots(1)$
Value of g at the poles
$g_p=\frac{GM}{R_p^2} \ldots(2)$
Value of $g$ at the equator
$g_e=\frac{GM}{R_c^2} \ldots(3)$
$\begin{aligned}But
R_p & < R_e \\
So,
g_p & >g_e
\end{aligned}$
Hence the value of $g$ at the poles will be higher.

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