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. $-\frac{Gm}{d}\left[3m^2+4\sqrt{2}M\right]$
• D. $-\frac{Gm}{d}\left[6m^2+4\sqrt{2}M\right]$

Answer 1

Answer: (A)

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