Question

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. $-\frac{ Gm }{ d }\left[6 m ^{2}+4 \sqrt{2} M \right]$

Answer 1

Answer: (A)

$-\frac{ Gm ^{2}}{ d } \times 4-\frac{ Gm ^{2}}{\sqrt{2} d } \times 2-\frac{ GMm }{ d } \times 4 \sqrt{2}$
$-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M ]$