If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth $α h (h ≪ R_{e})$ ) from the earth surface. The value of $α$ will be _____ .
(use $R_{e} = 6400 km$ )

Question

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth $α h (h ≪ R_{e})$ ) from the earth surface. The value of $α$ will be _____ .

(use $R_{e} = 6400 km$ )

Aicharya · Accepted Answer

Acceleration due to gravity at a height $h$ above the earth's surface is given by $g (1 - \frac{2 h}{R_{e}})$
And acceleration due to gravity at depth $d$ below the earth surface is given by $g (1 - \frac{d}{R_{e}})$ .
As $g_{above} = g_{below}$
So, $g (1 - \frac{2 h}{R_{e}}) = g (1 - \frac{d}{R_{e}})$
$\Rightarrow \frac{2 h}{R_{e}} = \frac{d}{R_{e}}$
$\Rightarrow α h = d$
Thus, the value of $α = 2$ .

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is…

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