Question

Find the potential energy of a system of four particle placed at the vertices of a square of side l. Also obtain te potential at the centre of the square

Answer 1

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For a mass of m potential energy of a test mass at distance r is given as (G⋅mr)

Total potential energy of the system is Gm2l×4+2⋅Gm2√2l or,4Gm2l+√2Gm2l ( Due to 4 mass at the vertices and 2 diagonally present,length of diagonal is √2l)

Distance of each mass from the centre is =length of diagonal/2 i.e l√2

So,potential energy at the centre for 4 such mass is ⎛⎜⎝Gml√2⋅4⎞⎟⎠ i.e 4√2Gml




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