Weight of a person on two planets with different masses

[Medgirl314]

Homework Statement

A person standing on the surface of a planet has a weight of 250 N. Suppose he goes to another planet that is the same size(volume) but twice the mass(more dense). What would his weight be on the second planet?

Homework Equations

g=Gme/re²

The Attempt at a Solution

Hopefully, it is logical to assume that the planets are approximate spheres. In the problem, it is stated that the volume for the two problems is equivalent. Since the volume formula for a sphere is 4/3∏*3r, we can assume that the radii are equivalent. G is a constant. Logic would seem to dictate that the answer is twice the force on the first planet, so the answer would be 1300. However, the answer just doesn't feel right. I can't place it, but it seems like the answer is too simple. Could someone please confirm my answer, or if it's wrong, tell me the problem?

Thanks so much.

 

[ZetaOfThree]

You're right. Good job.

 

[Medgirl314]

Thank you!

 

[HallsofIvy]

Though the volume of a sphere is \frac{4}{3}\pi r^3 not \frac{4}{3}\pi*3r!

 

[Medgirl314]

Thank you! I remember now, when I looked it up I must have misread it.

 

[Bandersnatch]

Wait, how did you get 1300 from doubling 250 again?

 

[Medgirl314]

I didn't. I somehow managed to type a 2 instead of a 6, even though the keys are nowhere near each other. Sorry for the confusion! Now it's a little concerning to me that others agreed when I typed the wrong number.

 

[Bandersnatch]

Now it's a little concerning to me that others agreed when I typed the wrong number.

No need. You've got it right.

 

[Medgirl314]

Okay, thank you!