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

StaticWaffles

1. The problem statement, all variables and given/known data
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?


2. Relevant equations
Fg=Gm1m2/r^2


3. 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/webpag...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...?