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A 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 of the n^th orbit and the particle's speed v in the orbit depend on n as

Asked in NEET 2025 · Bohr's rules in other systems

• (1) r∝ n^1/3; v∝ n^1/3
• (2) r∝ n^1/3; v∝ n^2/3
• (3) r∝ n^2/3; v∝ n^1/3
• (4) r∝ n^4/3; v∝ n^-1/3

Step-by-step solution

Why the other options are wrong

• (1) Makes vr grow as n^2/3, which breaks the quantisation rule mvr=(nh)/(2π).
• (2) Swaps the two exponents: then (v²)/r∝ n, so the force would grow with n instead of staying constant.
• (4) Keeps vr∝ n, but then (v²)/r∝ n⁻²: the force would weaken with n instead of staying constant.

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