Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?
A) 2r
B) r
C) $r \sqrt { 2 }$
D) 4r
E) $r / \sqrt { 2 }$

Question

Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?
A)  2r 
B)  r 
C) $r \sqrt { 2 }$
D)  4r 
E) $r / \sqrt { 2 }$

Quizplus · Accepted Answer

Surface gravity $g = \frac{Gm}{r^2}$, where $G$ is the gravitational constant, $m$ is the mass, and $r$ is the radius. If planet B has twice the mass of planet A ($2m$) and the same surface gravity, then $r_B = r_A \sqrt{2}$ to keep $g$ constant, because the radius must increase by the square root of the mass increase to maintain the same $g$.

Two Planets Have the Same Surface Gravity, but Planet B r2r \sqrt { 2 }r2​

Two Planets Have the Same Surface Gravity, but Planet B $r \sqrt { 2 }$