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
B)g/2
C)g/4
D)g/8
E)g/16

Question

Quizplus · Accepted Answer

The acceleration due to gravity on a planet is given by the formula: 
g = G M/R^2 
where G is the universal gravitational constant, M is the mass of the planet, and R is its radius. 
Comparing the planet with Earth: 
Mass of the planet, M = (1/2) Mass of Earth, Me 
Radius of the planet, R = 2 Radius of Earth, Re 
Putting the values in the formula: 
g = G (1/2) Me / (2Re)^2 
g = G Me / (2^2 x Re^2 x 2) 
g = G Me / (8 x Re^2) 
g = (1/8) G Me / Re^2 
g/8 = G M/R^2 
Therefore, the acceleration due to gravity on the planet is g/8 or (D).

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