Two particles are located on the x axis.Particle 1 has a mass m and is at the or

Question

Two particles are located on the x axis.Particle 1 has a mass m and is at the origin. Particle 2 has a mass2m and is at x=+L. A third particle is placed between particles 1and 2. Where on the x axis should the third particle be located sothat the magnitude of the gravitational force on both particle 1and particle 2 doubles? Express your answer in terms of L.
I am not even sure where to begin on this problem...other theplotting coordinates Two particles are located on the x axis.Particle 1 has a mass m and is at the origin. Particle 2 has a mass2m and is at x=+L. A third particle is placed between particles 1and 2. Where on the x axis should the third particle be located sothat the magnitude of the gravitational force on both particle 1and particle 2 doubles? Express your answer in terms of L.
I am not even sure where to begin on this problem...other theplotting coordinates

Explanation / Answer

first, the force on 1 is F1 = Gm(2m)/L^2 (positive means force to the right) force on 2 is F2 = -F1 (by newton;s 3rd law) now let the 3rd particle (of mass M) be placed at x=a (a>> unphysical because y is negativewhich means a is negative. so the first solution a=.414L is the right solution.

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