Question

In the arrangement shown in figure (15-E6), the string has a mass of 4.5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley ? Take $g=10m{s}^{-2}$.

Answer 1

Total length of string = 2 + 0.25 = 2.25 m Mass per unit length,

$m=\frac{4.5\times {10}^{-3}}{2.25}$

$=2\times {10}^{-3}kg/m$

$T=2g=20N$

Wave speed, $v=\sqrt{\left(\frac{T}{m}\right)}$

$\sqrt{\frac{20}{(2\times {10}^{-3})}}$

$=\sqrt{{10}^4}$

$={10}^{2}m/s=100m/s$

Time taken to reach the pulley,

$t=\left(\frac{s}{v}\right)$

$=\frac{2}{100}=0.02sec$