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 )

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/s2 (B) 9.65 m/s2 (C) 7.75 m/s2 (D) 5.25 m/s2

Tardigrade Admin · Accepted Answer

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 (1 - \frac{h}{R _{e}})

where

R_{e}

is radius of earth.

Given,

h = 100 km = 1 0^{5} m

R_{e} = 6400 km = 64 \times 1 0^{5} m

∴ g^{'} = g (1 - \frac{h}{R _{e}})

= 9.8 (1 - \frac{1 0 ^{5}}{64 \times 1 0 ^{5}})

= 9.8 (1 - \frac{1}{64}) = 9.65 m / s^{2}

Q. 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 $R = 6400 km$ )

$3.9 m / s^{2}$

$9.65 m / s^{2}$

$7.75 m / s^{2}$

$5.25 m / s^{2}$

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

3.9m/s2

9.65m/s2

7.75m/s2

5.25m/s2

Q. 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 $R = 6400 km$ )

$3.9 m / s^{2}$

$9.65 m / s^{2}$

$7.75 m / s^{2}$

$5.25 m / s^{2}$