The radii of two planets are respectively R1 and R2 and their densities are respectively ρ1 and ρ2. The ratio of the accelerations due to gravity at their surfaces is

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The radii of two planets are respectively $R_{1}$ and $R_{2}$ and their densities are respectively $ρ_{1}$ and $ρ_{2}$ . The ratio of the accelerations due to gravity at their surfaces is

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$g_{1} : g_{2} = R_{1} ρ_{1} : R_{2} ρ_{2}$

$g_{1} : g_{2} = R_{1} ρ_{2} : R_{2} ρ_{1}$

$g_{1} : g_{2} = \frac{ρ_{1}}{R_{1}^{2}} : \frac{ρ_{2}}{R_{2}^{2}}$

$g_{1} : g_{2} = R_{1} R_{2} : ρ_{1} ρ_{2}$

answer is D.

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Detailed Solution

$g = \frac{4}{3} πρGR ∴ \frac{g_{1}}{g_{2}} = \frac{R_{1} ρ_{1}}{R_{2} ρ_{2}}$

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