A central force is given as F(r) = −k / rⁿ, where k is a constant. What condition must n satisfy for a circular orbit to remain stable?

n must equal 2
n must be less than 3
n must be greater than 3
n must equal −1

Correct answer: n must be less than 3

Solution

For a circular orbit to remain stable under a central force F(r) = −k / rⁿ, the effective potential must have a minimum. This condition is satisfied when n < 3, as higher values lead to instability due to excessive inward force.

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