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Two planets have radii r₁ and r₂ and their densities are $ρ_{1}$ and $ρ_{2}$ , respectively. The ratio of acceleration due to gravity on them will be

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$r_{1}^{2} ρ_{1} : r_{2}^{2} ρ_{2}$

$r_{1} ρ_{2} : r_{2} ρ_{1}$

$r_{1} ρ_{1} : r_{2} ρ_{2}$

$r_{1} ρ_{1}^{2} : r_{2} ρ_{2}^{2}$

answer is A.

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Detailed Solution

$\begin{array}{l} g = \frac{GM}{r^{2}} = G \frac{4}{3} \frac{{πr}^{3} ρ}{r^{2}} = G \frac{4}{3} πrρ \\ \frac{g_{1}}{g_{2}} = \frac{r_{1} ρ_{1}}{r_{2} ρ_{2}} \end{array}$

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