NEET 2016 Phase 1 · PhysicsPrevious Year Question
A uniform rope of length L and mass m₁ hangs vertically from a rigid support, with a block of mass m₂ attached to its free (lower) end. A transverse pulse of wavelength λ₁ is produced at the lower end of the rope; when it reaches the top its wavelength is λ₂. The ratio λ₂/λ₁ is:
Answer: (B) √((m₁+m₂)/m₂). Answer: (B) Wave speed on a string v = √(T/μ).
- A.√(m₂/m₁)
- B.√((m₁+m₂)/m₂)✓
- C.√(m₁/m₂)
- D.√((m₁+m₂)/m₁)
Correct Answer
(B) √((m₁+m₂)/m₂)
Solution & Explanation
Answer: (B) Wave speed on a string v = √(T/μ). At the bottom the tension is T_bottom = m₂g; at the top it must support the whole rope plus block, T_top = (m₁+m₂)g. Frequency is conserved, so λ ∝ v ∝ √T. Thus λ₂/λ₁ = √(T_top/T_bottom) = √[(m₁+m₂)g / (m₂g)] = √((m₁+m₂)/m₂).
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