## Homework Equations

$$F=\frac{GMm}{d^2}$$

## 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!! Bystander
Homework Helper
Gold Member
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."

• 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!!

Bystander
Homework Helper
Gold Member
What equation are you solving?

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

Bystander
Homework Helper
Gold Member
WRITE the equation.

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

Bystander
Homework Helper
Gold Member
Can you eliminate GMm? Yes. Do so.

• Maged Saeed
Oh,,, I got it ...
Thanks

Bystander
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