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

Answer: (A)

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, $d=\frac{R_E}{2}$

$\therefore W^{\prime }=mg(1-\frac{R_E/2}{R_E})$

$=\frac{mg}{2}=\frac{W}{2}$

$=\frac{250N}{2}$

$=125N$