The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

Concept:

Acceleration due to gravity is defined as the acceleration in an object due to gravitational force. It's value on surface of earth is 9.8 m s^-2.

As we move away from surface of earth or towards the centre of earth, value of acceleration due to gravity decreases.

The value of acceleration due to gravity at a height h above the surface of earth is as follows:

\(g' = g \left(1-\frac{2h}{R_e}\right)\)

where g is value of acceleration due to gravity on surface of earth, R_e is radius of the earth.

The value of acceleration due to gravity at a depth d below the surface of earth is as follows:

\(g' = g (1-\frac{d}{R_e})\)

where g is value of acceleration due to gravity on surface of earth, Re is radius of the earth.

Calculation:

Given:

Height, h = 1 km

Above earth surface

\(g' = g \left(1-\frac{2h}{R_e}\right)\)

\(Δ g' = g\frac{2h}{R_e}\)   ---(1)

Below earth surface

\(g' = g (1-\frac{d}{R_e})\)

\(\Delta g = g \frac{d}{R_e}\)   ----(2)

From (1) & (2)

d = 2h

d = 2 × 1 km