Question

Assuming earth to be a sphere of a uniform density. What is the value of gravitational acceleration in a mine $100\, km$ below the earth's surface ?
(given $R=6400\, km$ )

• A. $3.9\, m/s^2$
• B. $9.65\, m/s^2$
• C. $7.75\, m/s^2$
• D. $5.25\, m/s^2$

Answer 1

Answer: (B)

As we go below the surface of the earth the value of acceleration due to gravity goes on decreasing and becomes zero at the centre of the earth.
Value of $g$ at a depth $h$ below the surface of earth is given by
$g'=g\left(1-\frac{h}{R_{e}}\right)$ where $R_{e}$ is radius of earth.

Given, $ h =100 \,km =10^{5} m $
$ R_{e} =6400\, km =64 \times 10^{5} m$
$\therefore g'=g\left(1-\frac{h}{R_{e}}\right) $
$=9.8\left(1-\frac{10^{5}}{64 \times 10^{5}}\right) $
$=9.8\left(1-\frac{1}{64}\right)=9.65\, m / s ^{2}$