Four particles of masses \(m\), \(2m\), \(3m\) and \(4m\) are placed in a clockwise manner at \(4\) corners of a square of side \(a\). Find the gravitational force acting on a particle of mass \(m\) placed at the center.

If the answer is in the form \(\frac { m\sqrt { n } G{ M }^{ 2 } }{ { a }^{ 2 } }\), find \(m+n\) .

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