Question

A body weighs $250N$ on the surface of the earth. How much will it weigh half way down to the centre of the earth.?

• A. $125N$
• B. $150N$
• C. $175N$
• D. $250N$.

Answer 1

The correct option is A $125N$

Let m be mass of a body.
$\therefore$ Weight of the body on the surface of the earth is W=mg=250N
Acceleration due to gravity at a depth d below the surface of the earth is $g^{\prime }=g(1-\frac{d}{R_E})$
Weight of the body at depth d is
$W^{\prime }=m{g}^{\prime }=mg(1-\frac{d}{R_E})$
Here, $d=\frac{R_E}{2}$
$\therefore W^{\prime }=mg(1-\frac{R_E/2}{R_E})=\frac{mg}{2}=\frac{W}{2}=\frac{250N}{2}=125N$