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Q.

Two planets have radii R₁ and R₂ and densities d₁ and d₂respectively. The ratio of the acceleration due to gravity on them will be :

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a

R₁d₁: R₂d₂

b

R₁d₂: R₂d₁

c

$R_{1} d_{1}^{2} : R_{2} d_{2}^{2}$

d

$R_{1}^{2} d_{1} : R_{2}^{2} d_{2}$

answer is B.

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Detailed Solution

$g = \frac{GM}{R^{2}} = \frac{Gd (\frac{4}{3} {πR}^{3})}{R^{2}} = \frac{4 πGdR}{3} \Rightarrow \frac{g_{1}}{g_{2}} = \frac{d_{1} R_{1}}{d_{2} R_{2}}$

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