Question

A block of mass $5\text{kg}$ is hanging from the top of a cliff. Calculate the speed of wave along this string, if length of the string is $1\text{m}$ and mass of the string is $5\text{gms}$.
[Take $g=10{\text{m/s}}^2$]

• A. $90{\text{ms}}^{-1}$
• B. $100{\text{ms}}^{-1}$
• C. $50{\text{ms}}^{-1}$
• D. $110{\text{ms}}^{-1}$

Answer 1

The correct option is B $100{\text{ms}}^{-1}$

Mass per unit length of string $\mu$ is,

$\mu =\frac{5\times {10}^{-3}}{1}=0.005\text{kg/m}$

Tension in the string is,

$T=mg=5\times 10=50\text{N}$

Therefore, velocity of a transverse wave is,

$V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{50}{0.005}}=100{\text{ms}}^{-1}$

Hence, $\left(B\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{This question gives you concept about wave velocity, mass per unit length}\mu =m/l\end{array}$