Two planets A and B have the same average density. Their radii RA and RB are such that RA: RB = 3: 1. If gA and gB are the acceleration due to gravity at the surfaces of the planets, the gA: gB equals

Question

Two planets A and B have the same average density. Their radii RA and RB are such that RA: RB = 3: 1. If gA and gB are the acceleration due to gravity at the surfaces of the planets, the gA: gB equals (A) 3: 1 (B) 1: 3 (C) 9: 1 (D) 1: 9

Tardigrade Admin · Accepted Answer

Given, (RA/RB)=(3/1) and ρA=ρB ∵ Average density, ρ=(3 g/4 π R G) ∴ From Eq. (ii), ⇒ (3 gA/4 π RA G)=(3 gB/4 π RB G) ⇒ (gA/gB)=(RA/RB) From Eq. (i), (gA/gB)=(3/1)

Q. Two planets A and B have the same average density. Their radii $R_{A}$ and $R_{B}$ are such that $R_{A} : R_{B} = 3 : 1$ . If $g_{A}$ and $g_{B}$ are the acceleration due to gravity at the surfaces of the planets, the $g_{A} : g_{B}$ equals

3 : 1

1 : 3

9 : 1

1 : 9

$3 : 1$

Q. Two planets A and B have the same average density. Their radii RA​ and RB​ are such that RA​:RB​=3:1. If gA​ and gB​ are the acceleration due to gravity at the surfaces of the planets, the gA​:gB​ equals