# Circular Motion - Help

I'm having troubles with one of my homework questions, and I was wondering if someone could help me with it.

okay here it is...

Q: Two masses, object A and object B are located 2m apart from eachother, the mass of object a is m and the mass of object b is 4m.

Showing your calculations find the point between these two objects where a third object would experiance no gravitation force.

I'm really stuck on this question, any help would be very much appreciated.

"a third object would experiance no gravitation force."
what they mean is, no net gravitation force
imagine a particle C lying on the line connecting A and B - what is the force that C feels from A? what is the force that C feels from B?
What is the net force?

I dont understand that at all...

I would have thought I'd try and figure out what m was = to then, maybe do that... because from what I know I dont think I can figure out the net gravititional force from just what I was given...

A little more help? heh

Are you aware that the force for gravitation is
$$\vec{F}=-\frac{Gm_1m_2}{r^2}\hat{r}$$

You have two masses m and 4m and some unknown mass m_2, so the magnitude of the gravitational attraction between m and m_2 is
$$F_1=\frac{Gmm_2}{r_1^2}$$
where r_1 is the distance between m_2 and m. The strength of the gravitational attraction between 4m and m_2 is
$$F_2=\frac{G(4m)m_2}{r_2^2}$$
where r_2 is the distance between 4m and m_2. If m_2 lies along the line between 4m and m and the distance between m and 4m is R, then
R=r_1+r_2, so the second equation becomes
$$F_2=\frac{G(4m)m_2}{(R-r_1)^2}$$
If m_2 is right between A and B, then the forces act in opposite directions and so cancel each other out. When F_1-F_2=0, m_2 will feel no force.