Four particles each of mass M, are located at the vertices of a square with side

Question

Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is

Options:

A . −√32GML

B . −√64GML2

C . Zero

D . √32GML

Answer: Option A
:
A

Four Particles Each Of Mass M, Are Located At The Vertices O...

Potential due to a point mass M at a distance r is

\frac{- G M}{r}

Potential at the centre due to single mass =

\frac{- G M}{\frac{L}{\sqrt{2}}}

Potential at the centre due to all four masses

= - 4 \sqrt{2} \frac{G M}{L} = - \sqrt{32} \times \frac{G M}{L}

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