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  • Three particles each of mass m are placed at the corners of an equilateral triangle of side d. The potential energy of the systems isOption: 1 <img a

Three particles each of mass m are placed at the corners of an equilateral triangle of side d. The potential energy of the systems is

Option: 1

\mathrm{\frac{3 G m^2}{d}}


Option: 2

\mathrm{\frac{ G m^2}{d}}


Option: 3

\mathrm{-\frac{3 G m^2}{d}}


Option: 4

none of these


Answers (1)

For the system of two particles, gravitational energy is given as

\mathrm{\begin{aligned} & \mathrm{U}=-\mathrm{G} \mathrm{m}_1 \mathrm{~m}_2 / \mathrm{r} \\ & \mathrm{U}_{\mathrm{A}}=\mathrm{U}_{12}+\mathrm{U}_{23}+\mathrm{U}_{31} \\ & \mathrm{U}_{\mathrm{A}}=-3 \frac{\mathrm{GMm}}{\mathrm{d}}=-\frac{3 \mathrm{Gm}^2}{\mathrm{~d}} \end{aligned}}

Therefore (C).

Posted by

Sumit Saini

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