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PART - 2 CH - 14 Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 14 Waves2 Marks
Question
A disturbance pulse takes 0.2 second to travel across a long wire and return. Tension is created in the wire by continuously hanging a weight 100 times the total weight of the wire on a pulley. Find the total length of the wire. Here g = 9.8 m/s.
✓

Answer

For the velocity of non-progressive wave.
$ \begin{aligned} v & =\sqrt{\frac{T}{m}} \\ v & =\sqrt{\frac{m \times l \times 100 \times g}{m}} \\ & {[\because \text { Total weight of wire }=(m l) g] } \\ \therefore v & =\sqrt{100 l g}\ldots\ldots (1) \end{aligned} $
Given : $\quad t=0.2=\frac{2 l}{ v }=\frac{2 l}{\sqrt{100 l g}}$
Put value from equation (1)
Taking square both side
$ \Rightarrow \quad(0.2)^2=\frac{4 l^2}{100 l g} $
$\Rightarrow \quad 0.04=\frac{4 l^2}{100 l g}$
$\Rightarrow \quad 0.04 \times 100=\frac{4 l}{g}$
$\begin{array}{ll}\Rightarrow & 4=\frac{4 l}{g} \\ \Rightarrow & l=g=9.8 meter\end{array}$

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