Question

The value of $g$at the center of the earth is ____

Answer 1

Acceleration due to gravity:

1. The acceleration of a body due to the gravitational force of attraction is called acceleration due to gravity '$g$'.

2. The equation for acceleration due to gravity at a depth $d$ is given by : $g^{\text{'}}=g\left(1-\frac{d}{R}\right)$

$g^{\text{'}}$⇢ Acceleration due to gravity at a depth

$g$⇢ Acceleration due to gravity near the surface

$d$⇢ Depth from the surface of Earth

$R$⇢ The radius of the planet

3. At the center of the Earth, the value of $d$ is equal to the value of the radius of Earth $R$ $\left(d=R\right)$.

Putting the value of $d$ in the equation $g^{\text{'}}=g\left(1-\frac{d}{R}\right)$.

$g^{\text{'}}=g\left(1-\frac{R}{R}\right)$

$g^{\text{'}}=g\left(1-1\right)$

$g^{\text{'}}=0$

Thus, acceleration due to gravity will be zero at that point.

Hence, the value of $g$ at the center of the earth is zero.