Two planets have radii r₁ and r₂ and their densities p₁ and p₂ respectively. ratio of accele

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7.Gravitation

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The two planets have radii $r_1$ and $r_2$ and their densities $p_1$ and $p_2$ respectively. The ratio of acceleration due to gravity on them will be

A

$r_1 p_1 : r_2 p_2$

B

$r_1 p_1^2 : r_2 p_2^2$

C

$r_1^2 p_1 : r_2^2 p_2$

D

$r_1 p_2 : r_2 p_1$

Solution

$g=\frac{G M}{r^{2}}=G \cdot \frac{4}{3} \frac{\pi r^{3} p}{r^{2}}=G \cdot \frac{4}{3} \pi r p$

$\therefore \quad \frac{g_{1}}{g_{2}}=\frac{r_{1} p_{1}}{r_{2} p_{2}}$

Standard 11

Physics

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