The potential energy of gravitational interaction of a point mass m and a thin uniform rod of mass M and length L ,if they are located along the straight line at a distance 'a' from each other?

1 Answer
Apr 22, 2017

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For this set up, we get the potential gravitational energy #dU# of the system, ie interaction between:

  • small element of width #dx# and mass #dM#; and

  • the mass m.

#dU = - (G \ m \ dM)/( a+ x)#

And #dM = M/L dx#

So #U = - (G m M)/L int_(x = 0)^L dx/( a+ x)#

#= -(G m M)/L ln (1+ L/a)#

With a point mass assumption and the same set up:

#U = - (GmM)/(a + L/2)#

They don't look that similar but if you play around with expansions or plot they do look alike.