Four particles each of mass 1 kg are at the four corners of a square of side 1 m. The work done to move one of the particles to infinity.
Given,m=1kg mass of each particle
a=1m side of square.
d=√2a=√2m diagonal of square.
From the figure,
The initial potential energy of the system,
Ui=(−4Gm2a)+(−2Gm2√2a)
Ui=−(2√2+1√2)2Gm2a. . . . (1)
When one mass is removed,
The final potential energy of the system,
Uf=(−2Gm2a)+(−Gm2√2a)
Uf=−(2√2+1√2)Gm2a. . . . (2)
The work done, W=Uf−Ui
W=−Gm2a(2√2+1√2)+2Gm2a(2√2+1√2)
W=(2√2+1√2)Gm2a
W=(2√2+1√2)G(1)21
W=(2√2+1√2)G