Which one of the following expressions gives the acceleration due to gravity at a…

PHYSICS · Single correct · CBSE · Physics · Gravitation · Gravitation

Problem

Which one of the following expressions gives the acceleration due to gravity

g_d

at a depth

d

below Earth’s surface (where

d\ll R_{\mathrm E}

) in terms of the surface value

g

? (a)

g_d = g\left(1-\dfrac{2d}{R_{\mathrm E}}\right)

(b)

g_d = g\left(1-\dfrac{d}{R_{\mathrm E}}\right)

(c)

g_d = g\left(1-\left(\dfrac{d}{R_{\mathrm E}}\right)^{2}\right)

(d)

g_d = g\left(\dfrac{R_{\mathrm E}}{R_{\mathrm E}-d}\right)^{2}