2013: Problem 13

Topic: Gravity
Concepts: Angular kinematics, Circular orbits

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Solution:

If the ring is part of Saturn, then it rotates together with the planet i.e. has the same angular velocity $\omega$. From angular kinematics,

$$\omega=\frac{v}{r}$$

$$v \propto r$$

If the ring is a satellite of Saturn, then it moves at the velocity of a circular orbit which is

$$v=\sqrt{\frac{GM}{r}}$$

$$v^2 \propto \frac{1}{r}$$

Thus, the answer is A.

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