Question

Three particles of equal mass 'm' are situated at the vertices of an equilateral triangle of side 'L'. The work done in increasing the side of the triangle to $2$L will be.

• A. $\frac{2G^{2}m}{2L}$
• 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 gravitational potential energy of the system $U_i=-\frac{Gmm}{L}-\frac{Gmm}{L}-\frac{Gmm}{L}=\frac{-3Gmm}{L}$

Initial gravitational potential energy of the system $U_f=-\frac{Gmm}{2L}-\frac{Gmm}{2L}-\frac{Gmm}{2L}=\frac{-3Gmm}{2L}$

Work done $W=U_f-U_i$

$⟹W=\frac{-3Gmm}{2L}-\left(\frac{-3Gmm}{L}\right)=\frac{3G{m}^2}{2L}$