Question

Akshay tied a rope of uniform mass between the two walls and disturbed it to vibrate. If the velocity of transverse wave in the rope, mass of rope and tension in the rope are $5m{s}^{-1},100g$and $1N$ respectively, then determine the length of the rope.

• A. 0.5 m
• B. 1.5 m
• C. 2 m
• D. 2.5 m

Answer 1

The correct option is D

2.5 m

Correct option is D: 2.5 m

Step 1: Given:

Velocity of transverse wave $\left(v\right)=5m{s}^{-1}$

Mass of rope $\left(M\right)=100g=100\times {10}^{-3}kg$

Tension in the rope $\left(T\right)=1\hspace{0.17em}N$

Find: Length of the rope

Step 2: Finding liner mass density of rope:

We know that, velocity of wave in rope is given by,

$v=\sqrt{\frac{T}{m}}$

Squaring both side,

$$\begin{gathered} v^2=\frac{T}{m}\Rightarrow m=\frac{T}{v^2} \\ \Rightarrow m=\frac{1}{5^2} \\ \Rightarrow m=0.04kg \end{gathered}$$

Step 3: Finding length of rope

again from the equation,

$$\begin{gathered} l=\frac{M}{m} \\ l=\frac{100\times {10}^{-3}kg}{0.04} \\ l=2.5m \end{gathered}$$

Hence, the length of the rope is 2.5 m