The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are and respectively. The ratio of acceleration due to gravity at their surfaces will be [2023]

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Solution

Q.
The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $ρ$ and $ρ / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_{A} : g_{B})$ will be [2023]

1 1 : 16

2 3 : 16

3 3 : 4

4 4 : 3

Ans.
(3)

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

$\frac{g_{A}}{g_{B}} = \frac{R \times ρ}{4 R \times \frac{ρ}{3}} = \frac{3}{4}$

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