Question

A transverse wave travels on a taut steel wire with a velocity of$𝑉$ when tension in it is $2.06\times {10}^4𝑁$. When the tension is changed to$T$, the velocity changed to $\frac{V}{2}$ The value of $T$ is close to

• A. $30.5\times {10}^4$
• B. $2.50\times {10}^4$
• C. $10.2\times {10}^2$
• D. $5.15\times {10}^3$

Answer 1

The correct option is D

$5.15\times {10}^3$

Step 1. Given data :

Velocity$V$ changes to$\frac{V}{2}$

Tension $2.06\times {10}^4𝑁$changes to$T$

Step 2. Find the value of $T$:

$$\begin{gathered} V=\sqrt{\frac{T}{\mu }} \\ {V}^2\alpha T \end{gathered}$$where $\mu$ is mass per unit length.

$$\begin{gathered} \frac{T_1}{T_2}={\left[\frac{V_1}{V_2}\right]}^2 \\ \frac{2.06\times {10}^4}{T}={\left[\frac{V}{\left({\displaystyle \frac{V}{2}}\right)}\right]}^2 \\ \frac{2.06\times {10}^4}{T}=4 \\ T=\frac{2.06\times {10}^4}{4} \\ T=0.515\times {10}^{4}N \\ T=5.15\times {10}^{4}N \end{gathered}$$

Hence, option (D) is correct .