question_answer

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

A)  \[\frac{3G{{m}^{2}}}{d}\]           

B)  \[\frac{G{{m}^{2}}}{d}\]

C)  \[\frac{-3G{{m}^{2}}}{d}\]         

D)  none of these

Correct Answer: C

Solution :

For the system of two particle gravitational energy is given as \[U=-G{{m}_{1}}{{m}_{2}}/r\] Now, for the system of mass \[{{U}_{A}}={{U}_{12}}+{{U}_{23}}+{{U}_{31}}\] \[{{U}_{A}}==-3\frac{GMm}{d}=\frac{3G{{m}^{2}}}{d}.\] negative sign resembles that the particles are bounded by their mutual gravitational field.