Question

The acceleration due to gravity at the poles and the equator is $g_p$ and $g_e$ respectively. If the earth is a sphere of radius $R_E$ and rotating about its axis with angular speed 0), then $g_p - g_e$ is given by

• A. $\frac{\omega^{2}}{R_{E}}$
• B. $\frac{\omega^{2}}{R^2_{E}}$
• C. $\omega^{2}R_{E}^2$
• D. $\omega^{2}R_{E}$

Answer 1

Answer: (D)

Acceleration due to gravity at a place of latitude $\lambda$ due to the rotation of earth is
$g'= g - R_{E}\omega^{2}cos^{2}\lambda$
At equator, $\lambda = 0^{\circ}, cos0^{\circ} = 1$
$\therefore g'= g_{ e}=g - R_{E}\omega^{2}$
At poles, $\lambda = 90^{\circ}, cos90^{\circ} = 0$
$\therefore g'=g_{p}=g$
$\therefore g_{p}-g_{e} = g - \left( g - R_{E}\omega^{2}\right) = R_{E}\omega^{2}$