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 :

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Gravitation

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) $2 : 3$
(B) $2 : 1$
(C) $3 : 4$ ✓ Correct
(D) $4 : 3$

Answer: (C)

Solution

Acceleration due to gravity at the surface is

g = \frac{4}{3} π GρR

. For planet B:

g_{B} = \frac{4}{3} π G (\frac{ρ}{2}) (1.5 R)

. For planet A:

g_{A} = \frac{4}{3} π GρR

. The ratio

\frac{g _{B}}{g _{A}} = \frac{ρ /2}{ρ} \times \frac{1.5 R}{R} = \frac{1}{2} \times 1.5 = \frac{3}{4}

, i.e., 3:4.

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Single correct option

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