Question

Two planets, planet A and planet B, have the same surface gravity. However, planet B has twice the radius of planet A. How does the mass of planet B compare to the mass of planet A?
A)The mass of planet B is one-fourth the mass of planet A.
B)The mass of planet B is twice the mass of planet A.
C)The mass of planet B is equal to the mass of planet A.
D)The mass of planet B is four times the mass of planet A.
E)The mass of planet B is one-half the mass of planet A.

Answer 1

Answer: D) The mass of planet B is four times the mass of planet A.

Explanation:

If the surface gravity is the same, this means that the attractive force exerted by both planets upon any body  on  the surface ,is the same.

This means that FgA and FgB are equal each other, so, applying the Universal Law of Gravitation to both planets, we can write:

FgA = G mMa / ra² = FgB = GmMb/rb²

Equating both sides, and simplyfing common terms, we have:

Ma/ra² = Mb/(2ra)²

Solving for Mb:

Mb = Ma . (4ra)² / ra² = 4 Ma