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)r/ $\sqrt { 2 }$
B)r
C)r $\sqrt { 2 }$
D)4r
E)2r

Question

Quizplus · Accepted Answer

The surface gravity $ g $ is given by $ g = \frac{GM}{r^2} $. Since both planets have the same surface gravity, $ \frac{GM_A}{r_A^2} = \frac{GM_B}{r_B^2} $. Given $ M_B = 2M_A $ and $ r_A = r $, solving for $ r_B $ gives $ r_B = r \sqrt{2} $.

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

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