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  4. The potential energy of 4 -particles each of mass 1 kg placed at the four vertices of a square of side length 1 m is

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Q. The potential energy of $ 4 $ -particles each of mass $ 1\,kg $ placed at the four vertices of a square of side length $ 1\,m $ is

AMUAMU 2010Gravitation

Solution:

Here, $AB=BC=CD=DA=1\,m$
image
$BD=AC$
$=\sqrt{1^{2}+1^{2}}$
$=\sqrt{2}m$
Total potential energy
$+\left[\frac{-G\times1\times1}{DA}\right]+\left[\frac{-G\times1\times1}{BD}\right]+\left[\frac{-G\times1\times1}{AC}\right]$
$=4\times\left[\frac{-G\times1\times1}{1}\right]+2\left[\frac{-G\times1\times1}{\sqrt{2}}\right]$
$=-5.4\,G$