Question

$3$ identical bodies of mass m are at the corners of an equilateral triangle of side $L$. Work done in moving them such that the side of the equilateral triangle becomes doubled is

• A. $\frac{2G{m}^2}{2L}$
• B. $\frac{G{m}^2}{2L}$
• C. $\frac{3G{m}^2}{2L}$
• D. $\frac{3G{m}^2}{L}$

Answer 1

The correct option is C $\frac{3G{m}^2}{2L}$

Initial potential energy, $U_i=\frac{-3G{m}^2}{L}$

Final potential energy, $U_f=-\frac{3G{m}^2}{2L}$

Work done, $W=U_f-U_i=-\frac{3G{m}^2}{2L}-(-\frac{3G{m}^2}{L})=\frac{3G{m}^2}{2L}$