A uniform wire $20 \mathrm{~m}$ long and weighing $50 \mathrm{~N}$ hangs vertically. The speed of the wave…
A uniform wire $20 \mathrm{~m}$ long and weighing $50 \mathrm{~N}$ hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity $=\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
$4 \mathrm{~ms}^{-1}$
$10 \sqrt{2} \mathrm{~ms}^{-1}$
$10 \mathrm{~ms}^{-1}$
Zero $\mathrm{ms}^{-1}$
Solution
$\mathrm{m}=\frac{50}{10}=5 \mathrm{~kg}$
$(\because \mathrm{W}=\mathrm{mg})$
Tension in the mid-point of the wire is:
$\mathrm{T}=\frac{\mathrm{m}}{2} \mathrm{~g}=\frac{5}{2} \times 10=25 \mathrm{~N}$
$\therefore \quad$ Speed of the wave at mid-point of the wire is:
$\begin{aligned}
\mathrm{v} & =\sqrt{\frac{\mathrm{T}}{\mu}}=\sqrt{\frac{25}{\left(\frac{5}{20}\right)}} \quad\left(\because \mu=\frac{\mathrm{m}}{\mathrm{L}}\right) \\
\therefore \quad \mathrm{v} & =10 \mathrm{~m} / \mathrm{s}
\end{aligned}$