The density of a planet is three times that of earth and radius 2.5 times that of earth. If g p and g e represents acceleration due to gravity on planet and earth respectively then ratio g p to

Question

The density of a planet is three times that of earth and radius 2.5 times that of earth. If g p ​ and g e ​ represents acceleration due to gravity on planet and earth respectively then ratio g p ​ to g e ​ is

TestHub · Accepted Answer

The acceleration due to gravity on the surface of a planet is given by

$g = \frac{GM}{R ^{2}}$

Substituting the mass of the planet $M = \frac{4}{3} π R^{3} ρ$ , we get

$g = \frac{G}{R ^{2}} (\frac{4}{3} π R^{3} ρ) = \frac{4}{3} π GRρ$

This implies that $g \propto Rρ$ .

The ratio of acceleration due to gravity on the planet to that on Earth is

$\frac{g _{p}}{g _{e}} = \frac{R _{p} ρ _{p}}{R _{e} ρ _{e}}$

Given that $ρ_{p} = 3 ρ_{e}$ and $R_{p} = 2.5 R_{e}$ , substituting these values yields

$\frac{g _{p}}{g _{e}} = (2.5) \times (3) = 7.5$

Answer: $7.5$

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