Mean Density of the Earth – Rankers Physics
Topic: Gravitation
Subtopic: Acceleration Due to Gravity and its variation

Mean Density of the Earth

If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be
\(\frac{3g}{4\pi RG}\)
\(\frac{4\pi G}{3gR}\)
\(\frac{\pi RG}{12g}\)
\(\frac{3\pi R}{4gG}\)

Solution:

We know \(g = \frac{G M}{R^2} = \frac{G}{R^2} \left(\frac{4}{3}\pi R^3 \rho\right) = \frac{4}{3}\pi RG\rho\). Solving for density, \(\rho = \frac{3g}{4\pi RG}\).

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