Question
In the arrangement shown in figure, the string has a mass of $4.5g$. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? Take $g = 10m/s^2$.

Answer



Total length of string $2+0.25=2.25\text{mt}$
Mass per unit length $\text{m}=\frac{4.5\times10^{-3}}{2.25}=2\times10^{-3}\text{kg/m}$
$\text{T}=2\text{g}=20\text{N}$
Wave speed,
$\text{v}=\sqrt{\Big(\frac{\text{T}}{\text{m}}\Big)}=\sqrt{\frac{20}{(2\times10^{-3})}}=\sqrt{10^4}=10^2\text{m/s}=100\text{m/s}$
Time taken to reach the pully, $\text{t}=\Big(\frac{\text{s}}{\text{v}}\Big)=\frac{2}{100}=0.02\text{sec}.$

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