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**Four particles A,B,C and D each of mass m are kept at the corners of a square of side L. Now the particle D is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle during its movement is....?**

**Gravitational potential at point D:**

${V}_{1}=-\frac{Gm}{L}-\frac{Gm}{L}-\frac{Gm}{\sqrt{2}L}\phantom{\rule{0ex}{0ex}}=-\frac{Gm}{L}\left(2+\frac{1}{\sqrt{2}}\right)$

**Gravitational potential at infinity:**

${V}_{2}=0$

**Work done:**

$W=m\left({V}_{2}-{V}_{1}\right)\phantom{\rule{0ex}{0ex}}=m\left[0+\frac{Gm}{L}\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)\right]\phantom{\rule{0ex}{0ex}}=\frac{G{m}^{2}}{L}\left(\frac{2\sqrt{2}+1}{\sqrt{2}}\right)$

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