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 acceleration due to gravity on the planet in terms of g, the acceleration due to
Gravity at the surface of the earth?
A) g/8
B) g/16
C) g
D) g/4
E) g/2

Question

Quizplus · Accepted Answer

The acceleration due to gravity (g) is given by the formula $g = \frac{G M}{R^2}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is the radius of the planet. If the mass of the hypothetical planet is half that of Earth ($M/2$) and its radius is twice that of Earth ($2R$), the acceleration due to gravity on the planet would be $g' = \frac{G (M/2)}{(2R)^2} = \frac{G M}{4R^2} \cdot \frac{1}{2} = \frac{g}{8}$, where $g = \frac{G M}{R^2}$ is the acceleration due to gravity on Earth.

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