Question

Suppose earth's mass increased but earth's diameter didn't change. Describe how the gravitational force between Earth and the object on its surface would change.

Answer 1

Answer:

It increases proportionally

Explanation:

The gravitational force between the Earth and an object on its surface is given by

$F=G\frac{Mm}{R^2}$

where

G is the gravitational constant

M is the Earth's mass

m is the mass of the object

R is the Earth's radius

In this problem, the Earth's mass is increased, while the diameter (and therefore, the radius) doesn't change. From the equation, we see that the gravitational force is directly proportional to the Earth's mass: therefore, if the mass is increased, the force will increase as well by the same proportion (for example, if the mass is doubled, the force will double as well)

Answer 2

Answer:

In this problem, the Earth's mass is increased, while the diameter (and therefore, the radius) doesn't change. From the equation, we see that the gravitational force is directly proportional to the Earth's mass: therefore, if the mass is increased, the force will increase as well by the same proportion (for example, if the mass is doubled, the force will double as well)

Explanation:

The gravitational force between the Earth and an object on its surface is given by

where

G is the gravitational constant

M is the Earth's mass

m is the mass of the object

R is the Earth's radius