Question

In the arrangement shown in figure,the string has 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 $2+0.25=2.25mt$

Mass per unit length $m=\frac{4.5\times {10}^{-3}}{2.25}=2\times {10}^{-3}kg/m$

Tension in the string is:

$T=2g=20N$

Wave speed , $v=\sqrt{\left(T/m\right)}=\sqrt{20}/\left(2/{10}^{-3}\right)=\sqrt{{10}^4}={10}^{2}m/s=100m/s$

Time taken to reach the pully, $t=\left(s/v\right)=2/100=0.02sec.$