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7.Gravitation
medium
Four spheres each of mass $m$ form a square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is
A
$-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M]$
B
$-\frac{ Gm }{ d }[(4+\sqrt{2}) M +4 \sqrt{2} M ]$
C
$-\frac{ Gm }{ d }\left[3 m ^{2}+4 \sqrt{2} M \right]$
D
$-\frac{ Gm }{ d }\left[6 m ^{2}+4 \sqrt{2 M }\right]$
(JEE MAIN-2022)
Solution
$-\frac{ Gm ^{2}}{ d } \times 4-\frac{ Gm ^{2}}{\sqrt{2} d } \times 2-\frac{ GMm }{ d } \times 4 \sqrt{2}$
$-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M ]$
Standard 11
Physics
