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

Question

Quizplus · Accepted Answer

The surface gravity of a planet is given by the equation:

g = G * M / R^2

where g is the surface gravity, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Since the two planets have the same surface gravity, we can set their equations equal to each other:

G * (mass of A) / (radius of A)^2 = G * (mass of B) / (radius of B)^2

The radius of planet B is twice that of planet A, so (radius of B)^2 = 4 * (radius of A)^2.

Substituting this into the equation above, we get:

G * m / (radius of A)^2 = G * (mass of B) / (4 * (radius of A)^2)

Simplifying, we get:

mass of B = 4 * m

Therefore, the mass of planet B is four times that of planet A, so the answer is D.

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

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