NEET 2025 · PhysicsAngular momentumPrevious Year Question
A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr's model is used to describe its motion, the radius of the nth orbit and the particle's speed v in the orbit depend on n as:
- A.r ∝ n^(2/3) ; v ∝ n^(1/3)✓
- B.r ∝ n^(4/3) ; v ∝ n^(-1/3)
- C.r ∝ n^(1/3) ; v ∝ n^(1/3)
- D.r ∝ n^(1/3) ; v ∝ n^(2/3)
Correct Answer
(A) r ∝ n^(2/3) ; v ∝ n^(1/3)
Solution & Explanation
Answer: (a) r ∝ n^(2/3) ; v ∝ n^(1/3) Solution: Constant central force F provides centripetal force: F = mv²/r → v² = Fr/m. Bohr quantization: mvr = nh/2π → v = nh/(2πmr). Substitute: (nh/2πmr)² = Fr/m → n²h²/(4π²m²r²) = Fr/m → r³ = n²h²/(4π²mF) → r ∝ n^(2/3). Then v² = Fr/m ∝ r ∝ n^(2/3) → v ∝ n^(1/3). So r ∝ n^(2/3), v ∝ n^(1/3).
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