Question

What is the magnitude of the gravitational force at the Earth's center?

Answer 1

Answer:

Given:

A body is taken to the center of the Earth

To find:

Gravitational force at that point

Concept:

At a depth "d" from the earth surface, the new gravitational force is given by the following formula :

$g2 \: = g(1 - \dfrac{d}{R} )$

where, d => depth, and R => radius of Earth

Calculation:

At the centre of the Earth, the depth will be equal to R.

So g" = g {1- (R/R)}

=> g" = g { 1 - 1}

=> g" = 0 m/s²

So the gravitational force will be zero at the centre of the Earth.