question_answer

If three particles each of mass M are placed at the comers of an equilateral triangle of side a, the potential energy of the system and the work done if the side of the triangle is changed from a to \[2a\], are:

A) \[\frac{3GM}{{{a}^{2}}}\,,\,\,\frac{3GM}{2a}\]                       

B) \[-\frac{3G{{M}^{2}}}{a}\,,\,\,\frac{3G{{M}^{2}}}{2a}\]

C) \[-\frac{3G{{M}^{2}}}{{{a}^{2}}}\,,\,\,\frac{3G{{M}^{2}}}{4{{a}^{2}}}\]

D) \[-\frac{3G{{M}^{2}}}{a}\,,\,\,\frac{3GM}{2a}\]

Correct Answer: B

Solution :

\[{{U}_{initial}}\,\,=\,\,3\left( \frac{-G{{M}^{2}}}{a} \right)\] \[{{U}_{final}}\,\,=\,\frac{-3G{{M}^{2}}}{2a}\] \[w=\Delta u={{U}_{f}}-{{U}_{i}}\,=\,\,\frac{3}{2}\,\frac{G{{M}^{2}}}{a}\]