Two planets A and B of radii R and 1.5 R have densities and respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]

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Solution

Q.
Two planets A and B of radii R and 1.5 R have densities $ρ$ and $ρ / 2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is [2023]

1 2 : 3

2 2 : 1

3 3 : 4

4 4 : 3

Ans.
(3)

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

$∴$ $\frac{g_{2}}{g_{1}} = \frac{ρ_{2}}{ρ_{1}} \times \frac{R_{2}}{R_{1}} = \frac{1}{2} \times 1.5 = \frac{3}{4}$

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