Q 11-14-011NEETJEE MainMedium
A uniform rope of mass $m$ and length $L$ hangs from a ceiling. The speed of a transverse pulse at a distance $x$ from its lower end is
Answer: (C) $\sqrt{gx}$
Concept. $v = \sqrt{\dfrac{T}{\mu}}$, where the tension at a point supports the rope below it.
Step 1. Tension at height $x$. $T = \dfrac{m}{L}xg$.
Step 2. Speed. With $\mu = \dfrac{m}{L}$:
$$v = \sqrt{\frac{(m/L)xg}{m/L}} = \sqrt{gx}$$
Answer. $\sqrt{gx}$ (Option C).
Solution by Sreeraj P, M.Sc Physics