Question

A body weights $ 500\,N $ on the surface of the earth. How much would it weigh half way below the surface of the earth?

• A. 1000 N
• B. 500 N
• C. 250 N
• D. 125 N

Answer 1

Answer: (C)

Value of acceleration due to gravity decreases on going below the surface of the earth.
weight ( $w$ ) of a body is defined as product of mass $(m)$ and acceleration due to gravity $(g)$
$w=m g$
The value of $g$ below the surface of earth at a distance $h$ is given by
$g'=g\left(1-\frac{h}{R}\right)$
$\Rightarrow W'=W\left(1-\frac{h}{R}\right)$
Given, $h=\frac{R}{2}, W=500\, N$
$W'=500\left(1-\frac{1}{2}\right)$
$=\frac{500}{2}=250\, N$