The value of acceleration due to gravity at a | vedclass

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(B) The value of acceleration due to gravity at height $h = 10 \,km$ is given by $g_h = g(1 - \frac{2h}{R_e}) = x$,where $R_e$ is the radius of the Ea

Vedclass · Accepted Answer

$20$

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(B) The value of acceleration due to gravity at height $h = 10 \,km$ is given by $g_h = g(1 - \frac{2h}{R_e}) = x$,where $R_e$ is the radius of the Earth. At a depth $d$ below the surface,the acceleration due to gravity is given by $g_d = g(1 - \frac{d}{R_e}) = x$. Equating the two expressions for $x$: $g(1 - \frac{2h}{R_e}) = g(1 - \frac{d}{R_e})$ $1 - \frac{2h}{R_e} = 1 - \frac{d}{R_e}$ $\frac{2h}{R_e} = \frac{d}{R_e}$ $d = 2h$. Given $h = 10 \,km$,we get $d = 2 	imes 10 \,km = 20 \,km$.

The value of acceleration due to gravity at a height of $10 \,km$ from the surface of the Earth is $x$. At what depth inside the Earth is the value of the acceleration due to gravity the same value $x$ (in $\,km$)?

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