A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.What is the free-fall acceleration on the planet in terms of g,the free-fall acceleration at the surface of the earth?
A)g
B)g/2
C)g/4
D)g/8
E)g/16

Question

Quizplus · Accepted Answer

The formula for free-fall acceleration at the surface of a planet is:

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.

In this case, the planet has a mass of one-half that of the earth (M = 1/2Me) and a radius of twice that of the earth (R = 2Re).

Substituting these values into the formula, we get:

g = G(1/2Me)/(2Re)^2
g = GMe/8Re^2
g/8

Therefore, the free-fall acceleration on the hypothetical planet is one-eighth of the free-fall acceleration at the surface of the earth, or g/8. The correct choice is D.

A Hypothetical Planet Has a Mass of One-Half That of the Earth