Question

A body of mass m is taken to the bottom of a deep mine. Then ___

• A. Its mass increases
• B. Its mass decreases
• C. Its weight increases
• D. Its weight decreases

Answer 1

The correct option is D

Its weight decreases

The weight of a body is proportional to the value of acceleration due to gravity (g) at a point.

$g=\frac{Gm}{r^2}$

Hence the acceleration due to gravity depends on the mass of earth and the distance of the body from the centre of the earth.

Assuming the density of the earth is fixed, the mass of the earth depends only on the volume. The volume of a sphere is proportional to the cube of its radius.

Hence if the object is at a depth where the distance from the centre of the earth is r, then the volume and hence the mass is proportional to $r^3$.

This means $g\propto \frac{r^3}{r^2}$.

Hence, $g\propto r$.

If the depth of the object increases, r decreases causing g to reduce and hence the weight reduces.