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The mean density of earth is___

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Proportional to the radius of the Earth

Proportional to the mass of the earth

Is a constant

None of these

answer is C.

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Detailed Solution

The mean density of earth is a constant value.
Density of any object is given by,

ρ = \frac{mass}{volume}

\Rightarrow ρ = \frac{M}{\frac{4 π}{3} R^{3}}

\Rightarrow ρ = \frac{3 M}{4 π R^{3}} . . . . . . . . . . . . . \dots (1)

Given,
The mass of the Earth,

M = 6 \times 10^{24} kg

The Radius of the Earth,

R = 6400 km

The mean density of Earth is calculated by substituting the given values in equation (1).

ρ = \frac{3 \times 6 \times 10^{24}}{4 \times 3.14 \times {(6.4 \times 10^{6})}^{3}}

\Rightarrow ρ = 5.5 \times 10^{3} kg m^{- 3}

As a result, the density of the earth is a constant because the quantities on which it is dependent are constants.

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