Question

The potential energy of a system of two particles is given by u(x)=a/x2-b/x. Find minimum potential energy of the system, where x is the distance of separation and a, b are positive constants.

Answer 1

I think you probably mean:
U = a/x^2 -b/x

dU/dx = -2ax/x^4 +b/x^2
where is that zero?

-2a/x^3 + b x/x^3 = 0
for zero x=2a/b
U = a/(4a^2/b^2)- b/(2a/b)
= a/(4a^2/b^2) - 2a/(4a^2/b^2)
= -a/ (4 a^2/b^2)
= -b^2/4a
or
U -a/x^2

Answer 2

Thanks