Classical Mechanics - Circular Motion

A particle of mass M moves in a circular orbit of radius r around a fixed point under the influence of an attractive force F = ^K⁄_r³, where K is a constant. If the potential energy of the particle is zero at an infinite distance from the force center, the total energy of the particle in the circular orbit is

A. − ^K⁄_r² 
B. − ^K⁄_2r²
C. 0
D. ^K⁄_2r²
E. ^K⁄_r²

(GR9277 #87)

Solution:

Attractive force = Centripetal Force
 ^K⁄_r³ = ^mv²⁄_r
mv² = ^K⁄_r²

Kinetic energy:  T = ½mv² = ^K⁄_2r²
Potential energy: V(r) = − ∫ F dr = −K ∫ ¹⁄_r³ dr = ^K⁄_2r²
Attractive force → negative potential energy, V(r) = − ^K⁄_2r²
Total energy:  T + V = ^K⁄_2r²  −  ^K⁄_2r² = 0

Answer: C