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  4. The value of g at a certain height h above the free surface of the earth is x / 4 where x is the value of g at the surface of the earth. The height h is

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Q. The value of $g$ at a certain height $h$ above the free surface of the earth is $x / 4$ where $x$ is the value of $g$ at the surface of the earth. The height $h$ is

Gravitation

Solution:

$x=\frac{G M}{R^{2}}$
Again, $\frac{x}{4}=\frac{G M}{(R+h)^{2}}$
or $x=G M\left(\frac{2}{R+h}\right)^{2}$
$\therefore \frac{1}{R^{2}}=\left(\frac{2}{R+h}\right)^{2}=\frac{2}{R+h}$
or $R+h=2 R$ or $h=R$