Question

If R is the radius of the earth and g is the acceleration due to gravity on the earth’s surface, the mean density of the earth is = ............…

Answer 1

Step-1: Given data:

Radius of Earth = R

Acceleration due to gravity = g

To find: mean density =?

Step-2: Formula used:

Given acceleration due to gravity,
$g=\frac{GM}{R^2}$

Step-3: Calculating density

We know the relation of gravity $g=GM{R}^2$

$\therefore M=g{R}^{2}G$ ………..(1)

The volume of the earth

$\frac{4}{3}{R}^3$

The average of the Earth, in general, is mainly density d,
$M=d\times V$ …………(2)

Solving equations 1 and 2,

$d=\frac{3g}{4\mathrm{\pi RG}}$

If R is the radius of the earth and g is the acceleration due to gravity on the earth’s surface, the mean density of the earth is, $d=\frac{3g}{4\mathrm{\pi RG}}$