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EEJ MAIN Physics QUESTION #7090
Question 1
A particle moves in a circular orbit under a central force $F \propto R^{-n}$. If the period is $T$, then:
  • $T \propto R^{(n+1)/2}$✔️
  • $T \propto R^{n/2}$
  • $T \propto R^{3/2}$
  • $T \propto R^{\frac{n}{2}+1}$
Correct Answer Explanation

Centripetal force $F = \frac{mv^2}{R} \propto \frac{1}{R^n}$.

  • $v^2 \propto \frac{1}{R^{n-1}} \implies v \propto R^{(1-n)/2}$
  • $T = \frac{2\pi R}{v} \propto \frac{R}{R^{(1-n)/2}} = R^{1 - (\frac{1-n}{2})} = R^{(n+1)/2}$.