Let omega be the angular velocity of the eart | vedclass

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(A) Let $\omega$ be the angular velocity of the earth's rotation about its axis.Let $g$ be the acceleration due to gravity at the poles.Let $R$ be the

Vedclass · Accepted Answer

$\frac{\omega^2 R^2}{g}$

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(A) Let $\omega$ be the angular velocity of the earth's rotation about its axis.Let $g$ be the acceleration due to gravity at the poles.Let $R$ be the radius of the earth.The effective acceleration due to gravity at the equator is $g_{eq} = g - \omega^2 R$.The acceleration due to gravity at a depth $d$ below the surface is $g_d = g(1 - \frac{d}{R})$.According to the problem,the readings are the same,so $g_{eq} = g_d$.$g - \omega^2 R = g(1 - \frac{d}{R})$$g - \omega^2 R = g - \frac{gd}{R}$$\omega^2 R = \frac{gd}{R}$$d = \frac{\omega^2 R^2}{g}$

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