Work done in changing configuration of a system of masses
Example: 3 identical bodies of mass m are at the corners of an equilateral triangle of side L. What is the amount of work done in moving them such that the side of the equilateral triangle becomes doubled?
Solution: Initial potential energy, Ui=L−3Gm2 Final potential energy, Uf=−2L3Gm2 Work done, W=Uf−Ui=−2L3Gm2−(−L3Gm2)=2L3Gm2
Work done in changing configuration of a system of continuous masses
Example: Four masses (each of m) are placed at the vertices of a regular pyramid (triangular base) of side ′a′. Find the work done by the system while taking them apart so that they form the pyramid of side ′2a′.
Solution: The initial gravitational potential is given as −6aGm2 Final gravitational potential is −62aGm2 Change in potential is −62aGm2−(−6aGm2) or 6aGm2−62aGm2=62aGm2=3aGm2 Thus the external work done would be −3aGm2