Question #169584

Consider a particle moving in a central force field


           f(u) = - ku2


using standard notation u =1/r. The quantity 


d2u/dθ2 + u


(a) is proportional to u2


(b) is proportional to u


(c) is a constant


(d) is proportional to 1/u


(e) none of these


1
Expert's answer
2021-03-08T08:18:13-0500
d2udθ2+u=f(u)mh2u2d2udθ2+u=ku2mh2u2d2udθ2+u=kmh2=const\frac{d^2u}{d\theta^2}+u=-\frac{f(u)}{mh^2u^2}\\ \frac{d^2u}{d\theta^2}+u=-\frac{ - ku^2}{mh^2u^2} \\ \frac{d^2u}{d\theta^2}+u=\frac{ k}{mh^2}=const

Answer: (c) is a constant

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