Mutual gravitational attraction of two 100mm iron spheres equals Earth's pull

[krnhseya]

Consider two iron spheres, each of diameter 100mm, which are just touching. At what distance r from the center of the Earth will the force of mutual attraction between the contacting spheres be equal to the force exerted by the Earth on one of the spheres?

Here's my work...

d = distance between center of spheres
r = distance between center of Earth to the center of sphere
me = mass of earth
m = mass of sphere=m1=m2

F = G(m^2)/(d^2)
= I get some number with (m^2)...so 1 unknown.

then I make this equal to...

F = G*me*m/(r^2)
= I get some number with m/(r^2)...so 2 unknowns.

I am confused as to what I am suppose to do beyond this...
Problem seems to be asking me to set 2 equations to equal to each other and solve for r but it won't work...what am I doing wrong?

Thank you.

 

[genneth]

It works: (use M for mass of earth)

$$\frac{Gm^2}{d^2} = \frac{GMm}{r^2}$$
$$\frac{m}{d^2} = \frac{M}{r^2}$$
$$r = \sqrt{\frac{M}{m}}d$$

Where you've given M, m and d.

 

[krnhseya]

m isn't given.
First thing that I wrote up there is the whole question.
Answer comes out to be a number.
How do I get the number if I have 2 unknowns. :(

I am thinking that there's something that I am missing that gets rid of that m so that I can cancel out m and just solve for r.

 

[genneth]

If they're iron, and you know the size, you can calculate the mass. Density of iron can be found in any data book.

 

[krnhseya]

OMG! There!
Now I see what I've missed.
I got the right answer. Thank you so much! :D