The gravitational potential energy of a system of three masscs $\mathrm{m}, 2 \mathrm{~m}$ and $3…
The gravitational potential energy of a system of three masscs $\mathrm{m}, 2 \mathrm{~m}$ and $3 \mathrm{~m}$ pläced at three vertices of equilateral triangle of side ' $a$ ' is
$-11 \frac{\mathrm{Gm}}{\mathrm{a}}$
$-11 \frac{G m^2}{a^2}$
$-11 \frac{G m^2}{a}$
$-11 \frac{G m}{a^2}$
Solution
The gravitational potential energy of a system is given by
$
\begin{aligned}
& \mathrm{U}=-\frac{\mathrm{G}}{\mathrm{a}}\left[2 \mathrm{~m}^2+6 \mathrm{~m}^2+3 \mathrm{~m}^2\right] \\
& \mathrm{U}=-11 \frac{\mathrm{Gm}^2}{\mathrm{a}}
\end{aligned}
$