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7.Gravitation
hard
Four particles each of mass $m$ are placed at the vertices of a square of side $l.$ The potential energy of the system is
A
$ - \frac{{\sqrt 2 G{m^2}}}{l}\left( {2 - \frac{1}{{\sqrt 2 }}} \right)$
B
$ - \frac{{2G{m^2}}}{l}\left( {2 + \frac{1}{{\sqrt 2 }}} \right)$
C
$ - \frac{{\sqrt 2 G{m^2}}}{l}\left( {\sqrt 2 + \frac{1}{{\sqrt 2 }}} \right)$
D
$ - \frac{{2G{m^2}}}{l}\left( {\sqrt 2 - \frac{1}{{\sqrt 2 }}} \right)$
Solution
$PE = \frac{{ – 4G{m^2}}}{l} – \frac{{2G{m^2}}}{{\sqrt 2 l}} = – \frac{{2G{m^2}}}{l}\left( {\sqrt 2 + \frac{1}{{\sqrt 2 }}} \right)$
Standard 11
Physics
