Suppose the mass of the Earth were doubled (Physics 12)

[StaticWaffles]

Homework Statement

Suppose the mass of the Earth were doubled , but it kept the same density and spherical shape. How would the weight of objects at the Earh's surface change?

Homework Equations

Fg=Gm1m2/r^2

The Attempt at a Solution

g=G2m/r^2
g=19.59817612

g/g(on Earth - 9.8)
=2

I know this is wrong because the textbook says the answer is 1.26 or 2^1/3.
I have no idea how to get this answer. I did find an online solution but they used equations that I have not been taught.

Here is a link to the online solution:
http://archives.evergreen.edu/webpages/curricular/2005-2006/PhyAstro/0506/HW/G6solns.pdf

If anyone can explain how to get this answer step by step that would be great.

 

[Simon Bridge]

If you double the mass, but keep the same density, what happens to the radius?

 

[StaticWaffles]

It would increase?

 

[Simon Bridge]

Did you increase the radius in your calculation?

 

[StaticWaffles]

No I didn't. So it would double as well?

 

[Simon Bridge]

Would it?
What is the relationship between mass and volume? volume and radius for a sphere?

 

[StaticWaffles]

I get it now. My Physics teacher explained it to me after school. Thank you!

 

[Simon Bridge]

Cool. Of course it would have been better if you'd reasoned it out yourself.
If you posted the answer here, you'd help someone else stuck on the same problem...?