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Q.
If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below its surface, then:
BHUBHU 2002
Solution:
The value of $g$ decreases on going above and below the earth's surface.
The value of $g$ at a height $h$ above the earth's surface of radius $R$ is given by
$g'=g\left(1-\frac{Z h}{R}\right)\,\,\,...(1)$
The value of $g$ at a depth $x$ below the surface of earth is given by
$ g''=g\left(1-\frac{x}{R}\right) \,\,\,...(2)$
Given, $g'=g''$
$\therefore g\left(1-\frac{2 h}{R}\right)=g\left(1-\frac{x}{R}\right)$
$\Rightarrow x=2 h$