An object moves in uniform circular motion. Its kinetic energy is directly proportional to:
I. centripetal force
II. radius of the circle
III. the period of circular motion
I took the universal gravitational law
G* m1 * m2 /r^2 = m2 * v^2/r
and then I rearranged for the kinetic energy of circular motion to get:
G * m1 * m2 /r = m2 * v^2 /2
The Attempt at a Solution
Looking at my equation, I was able to see that the bigger the centripetal force is, the more kinetic energy we have. I is an option.
As the radius gets bigger, the kinetic energy decreases, so II is out.
As the period of circular motion gets bigger, the velocity decreases, to the kinetic energy is not directly proportional.
Thus, I chose only I. However, the solutions say that the answer is I and II.
Why is this the case? Thanks a lot in advance!