JEE Main · PhysicsHard
A particle of mass $m$ moves in a potential field $U(x) = \frac{a}{x^2} - \frac{b}{x}$, where $a$ and $b$ are positive constants. What is the period of small oscillations about the stable equilibrium position?
- A.$2\pi \sqrt{\frac{ma^3}{b^4}}$
- B.$\pi \sqrt{\frac{ma^3}{b^4}}$
- C.$2\pi \sqrt{\frac{ma}{b^2}}$
- D.$4\pi \sqrt{\frac{ma^3}{b^4}}$
Show correct answer & step-by-step solution
Correct answer: A — $2\pi \sqrt{\frac{ma^3}{b^4}}$
Solution
Find the equilibrium position by setting . Then, calculate the second derivative at this point and use the formula .
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