Two planets have the same free-fall acceleration on the surface,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 free-fall acceleration on the surface of a planet can be given by:

g = GM/R^2

where 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 free-fall acceleration, we can write:

gA = gB

or

GMa/RA^2 = GMb/RB^2

Since planet B has twice the radius of planet A, we can write:

RB = 2RA

Substituting this into the above equation and simplifying, we get:

Mb = 4Ma

Therefore, the mass of planet B is 4 times the mass of planet A.

Thus, the correct choice is D.

Two Planets Have the Same Free-Fall Acceleration on the Surface,but 2\sqrt { 2 }2​

Two Planets Have the Same Free-Fall Acceleration on the Surface,but $\sqrt { 2 }$