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

Question

Two particles are located on the x-axis. Particle 1 hasa mass m and is at the origin. Particle 2 has a mass 2m andis at x= +L. Where on the x-axis should a third particle belocated so that the magnitude of the gravitational force on bothparticle 1 and particle 2 doubles? Express your answer in terms ofL. Note that there are 2 answers. answer: 0.414 L or -2.414 L Two particles are located on the x-axis. Particle 1 hasa mass m and is at the origin. Particle 2 has a mass 2m andis at x= +L. Where on the x-axis should a third particle belocated so that the magnitude of the gravitational force on bothparticle 1 and particle 2 doubles? Express your answer in terms ofL. Note that there are 2 answers. answer: 0.414 L or -2.414 L

Explanation / Answer

let the third particle be at x, and mass M force on 1 due 2 is Gm(2m)/L2, force on 1 due 3 isGmM/x2, to make force on 1 doubled, GmM/x2 = Gm(2m)/L2force on 2 due 1 isGm(2m)/L2, force on 2 due 3 is G(2m)M/(L -x)2, to make force on 2 doubled, G(2m)M/(L - x)2 = Gm(2m)/L2 compare these 2 equations we have 1/x2 = 2/(L - x)2 (L - x)2 = 2x2 L - x = ±2 x x = L/(2 + 1) = 0.414 L, or -L/(2 - 1) =-2.414 L

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