A uniform rope of length 12 m and mass 6 kg hangs vertically from the… | MHT CET 2021 (23 Sep, Shift 2)

Q26MHT CET 2021 · 23 SEP · SHIFT 2Difficult

Speed of Waves

A uniform rope of length $12\text{ m}$ and mass $6\text{ kg}$ hangs vertically from the rigid support. A block of mass $2\text{ kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\text{ m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

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Answer: (c)

Frequency stays the same along the rope, so $\lambda \propto v \propto \sqrt{T}$ .
Tension at the bottom: $T_1 = 2g$ ; at the top: $T_2 = (6+2)g = 8g$ .
$\dfrac{\lambda_2}{\lambda_1} = \sqrt{\dfrac{8g}{2g}} = 2 \Rightarrow \lambda_2 = 2 \times 0.06 = 0.12\text{ m}$
So the answer is (c) $0.12\text{ m}$ .

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