1. Dec 14, 2014

Maged Saeed

1. The problem statement, all variables and given/known data
Please look at the picture.

2. Relevant equations
$$F=\frac{GMm}{d^2}$$

3. The attempt at a solution
I'm stuck with this problem , because I cannot imagine it properly.
If I say that the mass m is in between the two masses , I cannot find d in the choices ,, Any help please!!

2. Dec 14, 2014

Bystander

The prompt gives you that the two large masses are separated by D, and that the small mass is somewhere between them, meaning that you are being asked for "d" in terms of "D."

3. Dec 14, 2014

Maged Saeed

The mass in between would have a net gravitational force equal to :
$$\frac{GMm}{d^2}-\frac{G(4M)m}{(D-d)^2}$$
and that should be ZERO.
Then solving for d won't lead to one of the choices!!

4. Dec 14, 2014

Bystander

What equation are you solving?

5. Dec 14, 2014

Maged Saeed

The equation is of the net gravitational force acting on smaller mass which should be zero.

6. Dec 14, 2014

Bystander

WRITE the equation.

7. Dec 14, 2014

Maged Saeed

$$\frac{GMm}{d^2}-\frac{G(4M)m}{(D-d)^2}=0$$

8. Dec 14, 2014

Bystander

Can you eliminate GMm? Yes. Do so.

9. Dec 14, 2014

Maged Saeed

Oh,,, I got it ...
Thanks

10. Dec 14, 2014

Bystander

Take things one step at a time, and they'll usually fall into place for you.