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?how to get there

  1. Jan 25, 2009 #1
    ??how to get there

    I tried to solve this question its from old exam and the answer is posted down but I didn't know how to get there please explain for me how we solve these kind of question??

    two particles with masses M and 4*M are separated by distance D what is the distance from the mass M for which the net gravitational force on a mass m is zero.

    the answer is (D/3)
     
  2. jcsd
  3. Jan 25, 2009 #2
    Re: ??how to get there

    What you want to do is to place an object of mass m between M and 4M so that the same force is applied by the two masses,but in opposite directions.

    F=G m1 m2/r^2 is the force formula

    notice that m=m1 and G cancel out
    Place the mass a distance x from M, then the mass is a distance (D-x) from 4M

    This leaves:
    M/x^2 = 4M/(D-x)^2

    Cancel the Ms, multiply and expand

    3x^2+2Dx-D^2 = 0
    use quadratic formula to get the solution for x.
     
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