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Physics · PYQ NEET UG 2025
हिन्दीA particle of mass \( m \) is moving around the origin with a constant force \( F \) pulling it towards the origin. If Bohr model is used to describe its motion, the radius \( r \) of the \( n^{\text{th}} \) orbit and the particle's speed \( v \) in the orbit depend on \( n \) as
Correct answer · Option 3
\( r \propto n^{2/3}; \quad v \propto n^{1/3} \)
Explanation
Given \( F = \text{constant} \). Centripetal force \( m v^2 / r = F \implies v \propto \sqrt{r} \). Quantization condition: \( m v r = \frac{n h}{2 \pi} \implies v r \propto n \). Solving gives \( r \propto n^{2/3} \) and \( v \propto n^{1/3} \).
