Two long strings A and B, each having linear mass density 1.2 10^… - Vidyadip

Question

Two long strings $A$ and $B,$ each having linear mass density $1.2 \times 10^{-2}\ kg/m$, are stretched by different tensions $4.8N$ and $7.5N$ respectively and are kept parallel to each other with their left ends at $x = 0.$ Wave pulses are produced on the strings at the left ends at $t = 0$ on string $A$ and at $t = 20\ ms$ on string $B.$ When and where will the pulse on $B$ overtake that on $A$?

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Answer

$\text{m}_\text{A}=1.2\times10^{-2}\text{ kg/m},\ \text{T}_\text{A}=4.8\text{N}$
$\Rightarrow\text{v}_\text{A}=\sqrt{\frac{\text{T}}{\text{m}}}=20\text{m/s}$
$\text{m}_\text{B}=1.2\times10^{-2}\text{kg/m},\ \text{T}_\text{B}=7.5\text{N}$
$\Rightarrow\text{V}_\text{B}=\sqrt{\frac{\text{T}}{\text{m}}}=25\text{m/s}$
$\text{t}=0$ in string $A$
$\text{t}_1=0+20\text{ ms}=20\times10^{-3}=0.02\text{ sec}$
In $0.02 \sec A$ has travelled $20\times0.02=0.4\text{mt}$
Relative speed between $A$ and $B =25-20=5\text{m/s}$
Time taken for $B$ for overtake $A =\frac{\text{s}}{\text{v}}=\frac{0.4}{5}=0.08\text{ sec}$

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