# Take the Centre of Mass, I Dare You!

Consider a homogenous rod of length $$L$$ and mass $$M$$, and a point-sized object of mass $$m$$, kept at a distance $$L$$ from one end of the rod, as shown in the figure.

Let the magnitude of force of gravitational attraction be $$F$$

If $$F=(\frac{a}{b})(\frac{GMm}{L^2})$$, where $$a,b$$ are coprime, natural numbers, find $$a+b$$

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