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: (a) 2: 1 (b) 2: 3 (c) 4: 3 (d) 3: 4

Answer: (d). g = 4/3π Gρ R, so g ∝ ρ R. (gB)/(gA) = ((ρ/2)(1.5R))/(ρ R) = 0.75 = 3/4 So the answer is (d) 3: 4.

Two planets A and B of radii R and 1.5 R have densities ρ and ρ/2… | JEE Main 2023 (13 Apr, Shift 2)

Q46JEE Main 2023 · 13 APR · SHIFT 2Easy

Acceleration Due to Gravity

Two planets A and B of radii $R$ and 1.5 R have densities $\rho$ and $\rho/2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to $A$ is:

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Answer: (d)

$g = \frac{4}{3}\pi G\rho R$ , so $g \propto \rho R$ .
$\frac{g_B}{g_A} = \frac{(\rho/2)(1.5R)}{\rho R} = 0.75 = \frac{3}{4}$
So the answer is (d) 3 : 4.

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