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
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
$ - \sqrt {32} \frac{{GM}}{L}$
$ - \sqrt {64} \frac{{GM}}{{{L^2}}}$
Zero
$\sqrt {32} \frac{{GM}}{L}$
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
Potential at the centre due to single mass = $\frac{{ - GM}}{{L/\sqrt 2 }}$
Potential at the centre due to all four masses
= $ - 4\frac{{GM}}{{L/\sqrt 2 }} - 4\sqrt 2 \frac{{GM}}{L}$
$ = - \sqrt {32} \times \frac{{GM}}{L}.$
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