Earth's density and its gravity

[new-tonian]

Homework Statement

Jack is tired of having to use 9.81 m/s^2 all the time to his calculations concerning gravity. He wants to use a round number 10 m/s^2. How much mass would have to be added to the Earth to make this happen? What would the new radius of the Earth be? Assume that the density of the Earth will remain the same. Where could you get the mass needed?

The Attempt at a Solution

All I have right now is the formula p=m/v. I know the volume of the Earth, its density and its mass, but I can't find the relationship between mass/density/volume and gravity.
I have to find the answer guided by the density formula only. I've tried to multiply the mass by the ratio of 9.81 and 10, but somehow the answer doesn't look right, and I won't know if it's right if I don't know how the 9.81 m/s^2 is derived from the density formula.

I'm not looking for the answer, just for hints as to how to approach this problem. Thanks!

 

[hage567]

What equation do you use for gravitational force? If you think about that and Newton's second law, you can see where "g" comes from.