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 (gA: gB) will be: (a) 3: 16 (b) 4: 3 (c) 1: 16 (d) 3: 4

Answer: (d). g = 4/3π Gρ R, so g ∝ ρ R. (gA)/(gB) = (ρ R)/((ρ/3)(4R)) = 3/4 So the answer is (d) 3: 4.

The radii of two planets 'A' and 'B' are 'R' and '4R' and their… | JEE Main 2023 (11 Apr, Shift 1)

Q47JEE Main 2023 · 11 APR · SHIFT 1Easy

Acceleration Due to Gravity

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be:

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Answer: (d)

$g = \frac{4}{3}\pi G\rho R$ , so $g \propto \rho R$ .
$\frac{g_A}{g_B} = \frac{\rho R}{(\rho/3)(4R)} = \frac{3}{4}$
So the answer is (d) 3 : 4.

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