Escape Speed from Planets with Different Radii

[vrobins1]

Homework Statement

The escape speed from the surface of the Earth is 11.2 km/s. What would be the escape speed be from another planet of the same density (mass per unit volume) as Earth but with a radius 5 times that of Earth's?

Homework Equations

I know I have to use v=sqrt2GM/R

The Attempt at a Solution

I wasn't really sure how to go about this problem, but I did v₁/v₂ = 11.2/v₂ = sqrt5

So I solved for v₂ by doing 11.2/(sqrt5) and I got 5.00879227.
I have tried 5, 5.0, and 5.009 as answer submissions and got them all incorrect. I am not even sure if I am setting the problem up right, so any guidance or hints would be much appreciated. Thanks!

 

[D H]

Homework Equations

I know I have to use v=sqrt2GM/R

The Attempt at a Solution

I wasn't really sure how to go about this problem, but I did v₁/v₂ = 11.2/v₂ = sqrt5

Rather than guessing, use the equation you supplied. It is indeed very relevant to the problem, but you didn't use it at all.

To go about using that equation you need to know each term involved in the equation. Which terms do you know, and which don't you know? Can you solve for the ones you don't know?

 

[ShawnD]

The escape speed from the surface of the Earth is 11.2 km/s. What would be the escape speed be from another planet of the same density (mass per unit volume) as Earth but with a radius 5 times that of Earth's?

Did you account for the new planet's mass? I think the volume of a sphere is (4/3)(pi)(r^3). A planet with 5x the radius is 125x as heavy. I don't actually know how to solve this problem, but this is probably important.

 

[D H]

Yes, it is, Shawn. This however, is homework and you shouldn't have given so much info, at least at the onset.