Answer to Question #169588 in Classical Mechanics for Rohan

Question

Consider a particle moving in a central force field 

f(u) = - ku³

using standard notations 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

Answer 1

Answer

According to centrel force motion

is given

$F(\frac{1}{u}) =-\frac{J^2u^2}{m}(\frac{d^2u}{d\theta^2}+u)$

Therefore when we get

$(\frac{d^2u}{d\theta^2}+u)=-F(\frac{1}{u})\frac{J^2u^2}{m}$

Therefore we can can say the quantity

$(\frac{d^2u}{d\theta^2}+u)$ is directly inversely proportional to u^2. so option e is correct.