At a height of 10 ,km above the surface of ea | vedclass

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Question

(d)

The value of acceleration due to gravity at a height $h$ is

$g_h=g\left(1-\frac{2 h}{R}\right)$

and at depth $d$ is

$g_d=g\left(1-\fra

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(d)

The value of acceleration due to gravity at a height $h$ is

$g_h=g\left(1-\frac{2 h}{R}ight)$

and at depth $d$ is

$g_d=g\left(1-\frac{d}{R}ight)$

It is given that, $g_h=g_d$

$\Rightarrow \quad g\left(1-\frac{2 h}{R}ight)=g\left(1-\frac{d}{R}ight)$

$\Rightarrow \quad \frac{2 h}{R}=\frac{d}{R}$

$\Rightarrow \quad d=2 h=2 	imes 10 \quad(\because h=10 \,km )$

$=20 \,km$

At a height of $10 \,km$ above the surface of earth, the value of acceleration due to gravity is the same as that of a particular depth below the surface of earth. Assuming uniform mass density for the earth, the depth is ............. $km$

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