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Q.
A body weighs $250 \,N$ on the surface of the earth. How much will it weigh half way down to the centre of the earth?
Gravitation
Solution:
Let $m$ be mass of a body.
$\therefore $ Weight of the body on the surface of the earth is
$W = mg = 250 \,N$
Acceleration due to gravity at a depth $d$ below the surface of the earth is
$g' = g(1 - \frac{d}{R_E})$
Weight of the body at depth $d$ is
$W' = mg' = mg(1 - \frac{d}{R_E})$
Here, $d = \frac{R_E}{2}$
$\therefore W' = mg(1 - \frac{R_E/2}{R_E})$
$ = \frac{mg}{2} = \frac{W}{2}$
$ = \frac{250\,N}{2}$
$ = 125\,N$