AP Physics C
posted by Tabetha .
One dimension. In the figure, two point particles are fixed on an x axis separated by distance d. Particle A has mass mA and particle B has mass 5.00 mA. A third particle C, of mass 62.0 mA, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero

well, B exerts a force G(mA)(5mA)/d^2 = 5GA^2/d^2
C exerts a force G(mA)(62mA)/x^2 = 62GA^2/x^2
we want the two forces to cancel (so C must be on the opposite side of A from B), so if A is at 0 and B is at d,
5/d^2 = 62/x^2
x^2 = 62d^2/5
x = d√(62/5)