(Solution) - The point masses m and 2m lie along the x axis -(2025 Original AI-Free Solution)

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The point masses m and 2m lie along the x-axis, with m at the origin and 2m at x = L. A third point mass M is moved along the x-axis.
(a) At what point is the net gravitational force on M due to the other two masses equal to zero?
(b) Sketch the x-component of the net force on M due to m and 2m, taking quantities to the right as positive. Include the regions x < 0, 0 < x < L, and x > L be especially careful to show the behavior of the graph on either side of x = 0 and x = L