About Gravitational Force

  • #1
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Homework Statement


Please look at the picture.

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!!
q23.jpg
 

Answers and Replies

  • #2
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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."
 
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  • #3
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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
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What equation are you solving?
 
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  • #5
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The equation is of the net gravitational force acting on smaller mass which should be zero.
 
  • #6
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WRITE the equation.
 
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  • #7
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$$\frac{GMm}{d^2}-\frac{G(4M)m}{(D-d)^2}=0$$
 
  • #8
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Can you eliminate GMm? Yes. Do so.
 
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  • #9
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Oh,,, I got it ...
Thanks
 
  • #10
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Take things one step at a time, and they'll usually fall into place for you.
 
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