Question

The radii of two planets are respectively R₁ and R₂ and their densities are respectively ρ₁ and ρ₂. The ratio of the accelerations due to gravity at their surfaces is
(a) $g_{1}:g_{2}=\frac{\rho_{1}}{R_{1}^{2}}:\frac{\rho_{2}}{R_{2}^{2}}$
(b) g₁ : g₂ = R₁R₂ : ρ₁ρ₂
(c) g₁ : g₂ = R₁ρ₂ : R₂ρ₁
(d) g₁ : g₂ = R₁ρ₁ : R₂ρ₂

Answer 1

a is the answer.

PLEASE MARK BRAINLIST.

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Answer 2

Answer:

D) g₁ : g₂ = R₁ρ₁ : R₂ρ₂

Explanation:

Acceleration due to gravity at the surface of planet = g = (4/3) GRπp

Planet 1; R = R and p = P

Thus,

g1 = (4/3) GRπP

Planet 2 ; R = 2R and p = P/2

Thus,  

g2 = (4/3) G2RπP/2 or 

g2 = (4/3) GRπP

Thus g1 = g2

Ratio will  = 1:1

Therefore, the ratio of the accelerations due to gravity at their surfaces is g₁ : g₂ = R₁ρ₁ : R₂ρ₂