Orbital velocity of a satellite revolving in a circular path close to the planet

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is directly propotional to the density of the planet

is directly propotional to the square root of density of the planet

is directly propotional to the square of density of planet

is inversely proportional to the square root of density of planet

answer is B.

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Detailed Solution

Orbital speed $V = \sqrt{\frac{G M}{r}}$

Where r = radius of orbit . If the orbit is very close to the surface of earth r $≃$ R = radius of planet.

M = Mass of planet $= \frac{4}{3} π R^{3} ρ$

Where ρ = density of planet.

$∴ V = \sqrt{\frac{G (\frac{4}{3} π R^{3} ρ)}{R}} = \sqrt{\frac{4}{3} π G \cdot ρ} R$

$∴ V \propto \sqrt{ρ} and V \propto R$

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