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## Homework Statement

Now calculate the total potential energy of the Plummer mass distribution. Hint:

The answer should depend only on G, M, and a

## Homework Equations

M(r)=Mr

^{3}/(r

^{2}+a

^{2})

^{3/2}

p(r)=3Ma

^{2}/4pie(r

^{2}+a

^{2})

^{5/2}

## The Attempt at a Solution

looking at my notes i find a formula to find total potential energy

U=-4pieG integral from 0 to R M(r)P(r)r dr

What i am confused about is that it says hint answer only depends on G M a, but what about the R from the integral? it also said in the problem that hint integral from o to infinity x

^{4}dx/(x

^{2}+1)

^{4}= pie/32

so looking at the hint integral, instead of doing integral from 0 to R would I just do it from 0 to infinity? That than would get rid of the R and just have answer of just G M a.

Is this right?

thanks