10. If the mass of the Earth is... increased by a factor of 2, then the Fgrav is by a factor of . ... increased by a factor of 3, then the Fgrav is by a factor of . ... decreased by a factor of 4, then the Fgrav is by a factor of .

If the mass of the Earth is increased by a factor of 2, then the Fgrav is increased by a factor of 2.

If the mass of the earth is increased by a factor of 3, then Fgrav is increased by a factor of 3.

If the mass of the earth is decreased by a factor of 4, then the Fgrav is decreased by a factor of 4

Explanation:

In order to solve this question, we must take into account that the force of gravity is given by the following formula:

So if the mass of the earth is increased by a factor of 2, this means that:

so:

Therefore:

When simplifying we end up with:

so if the mass of the Earth is increased by a factor of 2, then the Fgrav is increased by a factor of 2.

If the mass of the earth is increased by a factor of 3

So if the mass of the earth is increased by a factor of 2, this means that:

so:

Therefore:

When simplifying we end up with:

so if the mass of the Earth is increased by a factor of 3, then the Fgrav is increased by a factor of 3.

If the mass of the earth is decreased by a factor of 4

So if the mass of the earth is decreased by a factor of 4, this means that:

so:

Therefore:

When simplifying we end up with:

so if the mass of the Earth is decreased by a factor of 4, then the Fgrav is decreased by a factor of 4.