Two planets have the same free-fall acceleration on the surface,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 free-fall acceleration (g) is given by:

g = GM/R^2

Where G is the gravitational constant, M is the mass of the planet, and R is its radius.

Since the free-fall acceleration is the same on both planets, we can write:

gA = gB

GMa / Ra^2 = GMb / Rb^2

Ra^2 / Rb^2 = Mb / Ma

Since Mb = 2Ma, we have:

Ra^2 / Rb^2 = 2

Rb^2 = Ra^2 / 2

Taking the square root of both sides, we obtain:

Rb = Ra / √2

Therefore, the answer is C.

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 $\sqrt { 2 }$