The radii of two planets A and B are in the ratio 2: 3. Their densities are 3 ρ and 5 ρ respectively. The ratio of their acceleration due to gravity is: (a) 9: 4 (b) 9: 8 (c) 9: 10 (d) 2: 5

Answer: (d). g = 4/3π Gρ R, so g ∝ ρ R. (gA)/(gB) = (2 × 3ρ)/(3 × 5ρ) = 6/15 = 2/5 So the answer is (d) 2: 5.

The radii of two planets A and B are in the ratio 2: 3. Their… | JEE Main 2022 (30 Jun, Shift 1)

Q74JEE Main 2022 · 30 JUN · SHIFT 1Easy

Acceleration Due to Gravity

The radii of two planets A and B are in the ratio 2: 3. Their densities are 3 $\rho$ and 5 $\rho$ respectively. The ratio of their acceleration due to gravity is:

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Answer: (d)

$g = \frac{4}{3}\pi G\rho R$ , so $g \propto \rho R$ .
$\frac{g_A}{g_B} = \frac{2 \times 3\rho}{3 \times 5\rho} = \frac{6}{15} = \frac{2}{5}$
So the answer is (d) 2 : 5.

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