# Newton's law of gravitation, find the mass and radius of the sphere

1. Aug 2, 2017

### Sunsethorizon

1. The problem statement, all variables and given/known data
Two fully equal sphere's of lead are placed next to each other so that the gravitational force between sums up to 10N. Calculate mass and radius of the two sphere's.

2. Relevant equations
F=gm, F=GMm/r2 , V=4πr3/3 , ρ=m/V

3. The attempt at a solution
This has bugged me for quite some time now. With only gravitational force and density known, any attempt i do to calculate either mass or radius end's up with either two unknown variables or the wrong answer.
I am missing something crusial. Please Point me in the right direction :).

2. Aug 2, 2017

### Steven Thomas

When it says placed next to each other, does that mean the spheres are touching one another?
If so you can rewrite the one radii in terms of the other and you only have one unknown.

3. Aug 2, 2017

### Sunsethorizon

It acctually states that the spheres are placed so that the gravitational force sums up to 10N. It does not state that the two spheres are touching.

4. Aug 2, 2017

### ehild

The problem states that
What do you think "next to each other " can mean in this context?

5. Aug 2, 2017

### Steven Thomas

@Sunsethorizon If you attempt to solve assuming that they are touching, do you get the correct answer? Otherwise, as you say before, I think you will have two unknowns, both the mass / radius of he lead spheres and their separation.

6. Aug 2, 2017

### Sunsethorizon

If i assume that the two sphere's are touching. How can i use that to go forward when the gravitational forces between originate from each sphere's center.
it the two spheres touch, does that eliminate r from F=GMm/r2?

It probably means that the two spheres does touch. But i dont know how to proceed.

7. Aug 2, 2017

### ehild

No. The gravitational force between two spheres is as if all mass of each sphere was concentrated in the center.

8. Aug 2, 2017

### Steven Thomas

Let's assume they are touching. We call the radius of the spheres r and the separation between the two spheres (centre to centre) R. When they touch we have R = 2r. You can substitute this into the equation for the force of gravity, and substitute for the mass in terms of density and volume, then sub volume of a sphere. You will now have only one unknown, r.

Whether or not this turns out to be the correct answer I'm not sure, calculate it and let me know. If not, then our assumption that they touch was incorrect.

9. Aug 3, 2017

### Sunsethorizon

The two sphere's did touch, i finally solved it. Thanks for your kind help :)

Since m1=m2 , equation for force can be stated F=GM2/r2

with r=2r and substitute for mass the final equation is F=G(ρ4πr3/3)2/(2r)2 , solved for r does give the correct anwer for radius.