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Four particles of mass M are placed at the vertices of a square with side L. What is the gravitational potential due to this at the center of the square.
the length of each diagonal of the square is √2l. so here we get 4 particles with distances between any pair being l and 2 diagonal pairs for which the corresponding distance is √2l. Now, the P.E. of the system is U =[(-4Gm^2)/l-(2Gm^2)÷√2l] =(-5.41Gm^2)/lThe gravitational potential at the centre of the square is=4×[(-Gm)÷(√2l/2)=(-4√2Gm)÷l=(-5.64Gm)÷l (ans)
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