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What formula is used to determine the earth's mean density?

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\frac{3 g}{4 πGR}

\frac{8 g}{4 πGR}

\frac{6 g}{4 πGR}

\frac{4 g}{4 πGR}

answer is A.

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Detailed Solution

The mean density of earth is calculated using the expression

\frac{3 g}{4 πGR}

.
Density of a body of mass

M

and volume

V

is given by

density = \frac{mass}{volume}

= \frac{M}{\frac{4}{3} π R^{3}}

Let

M

be the mass of the earth and

R

be its radius.
The acceleration due to gravity is given by,

g = GM / R^{2}

Where,

G

is the universal gravitational constant.

mass of Earth, M = g R^{2} / G

The mean density of earth,

D_{E} = (g R^{2} / G) /

(

\frac{4}{3} π R^{3})

\Rightarrow D_{E} = \frac{3 g}{4 πGR}

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