Question

A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?
A)The acceleration due to gravity is g/9.
B)The acceleration due to gravity is g/3.
C)The acceleration due to gravity is g.
D)The acceleration due to gravity is 9g.
E)The acceleration due to gravity is 3g.
F)The acceleration due to gravity is g/27.

Answer 1

Answer:

F) The acceleration due to gravity is g/27

Explanation:

According to Newton gravitational law, the gravitational acceleration is directly proportional to the planet mass and inversely proportional to the square of distance.

Since our new planet has a mass of one-third of Earth's and radius 3 times of Earth's. This means the new planet is lighter and further away from the distance. This means g is first reduced by 3 due to smaller mass and then reduced by 9 due to square of 3 times the distance.

The gravitational acceleration on this new planet must be

$\frac{g/3}{3^2}$

$\frac{g}{27}$

So F) is the correct answer