Question

A particle moves under the influence of a central force given by F(r) = - k/ rⁿ. If the particle's orbit is circular and passes through the force center, show that n = 5.

Answer 1

$F(r)=-\frac k{r^n},$

$x^2+y^2=r^2,$

$U=\int Fdr=\frac{k}{(n-1)r^{n-1}},$

$F(r)=-\frac k{r^5}.$