The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If R is the radius of earth, then radius of t

Question

The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If R is the radius of earth, then radius of the planet would be

TestHub · Accepted Answer

The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R ^{2}}$ .

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

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

This implies $g \propto Rρ$ .

Given that $g_{p} = g_{e}$ and $ρ_{p} = 2 ρ_{e}$ .

Therefore, $R_{p} ρ_{p} = R_{e} ρ_{e}$

$R_{p} (2 ρ_{e}) = R ρ_{e}$

$R_{p} = \frac{R}{2}$

Answer: $R /2$

Physics - Gravitation Question with Solution | TestHub

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