Q 11-14-106JEE MainJEE Main 2020 (3 Sep, Shift 1)Medium
A uniform thin rope of length $12\ \text{m}$ and mass $6\ \text{kg}$ hangs vertically from a rigid support and a block of mass $2\ \text{kg}$ is attached to its free end. A transverse short wave train of wavelength $6\ \text{cm}$ is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?
Answer: (C) $12$
Tension at the bottom $= 2g$, at the top $= (2 + 6)g = 8g$.
The frequency stays the same, so $\lambda \propto v \propto \sqrt{T}$:
$$\lambda_{top} = 6\sqrt{\frac{8g}{2g}} = 12\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics