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The radii of two planets A and B are in ratio 2:3 .Their densities are $3 p$ and $5 p$ respectively. The ratio of the acceleration due to gravity on the surface of the respective planets is _______

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$9 : 4$

$2 : 5$

$9 : 10$

$9 : 8$

answer is D.

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Detailed Solution

$S i n c e g = \frac{G M}{R^{2}}$

$\Rightarrow g = \frac{G}{R^{2}} \times ρ \times \frac{4}{3} π R^{3}$

$\Rightarrow g \propto ρ R S o, \frac{g_{1}}{g_{2}} = \frac{ρ_{1}}{ρ_{2}} \times \frac{R_{1}}{R_{2}} = \frac{3}{5} \times \frac{2}{3} = \frac{2}{5}$

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