Question

In the figure the string has a mass $4.5\text{g}$. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? (Take $g=10{\text{ms}}^{-2})$

• A. $0.08\text{s}$
• B. $0.2\text{s}$
• C. $0.04\text{s}$
• D. $0.02\text{s}$

Answer 1

The correct option is D $0.02\text{s}$

The wave speed will be given by $v=\sqrt{\frac{T}{\mu }}$
where $\mu$ is mass per unit length of the string.
$\mu =\frac{4.5}{2.25}=2{\text{gm}}^{-1}=2\times {10}^3{\text{kgm}}^{-1}$
$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{20}{2\times {10}^{-3}}}=100{\text{ms}}^{-1}$
Applying the equation of motion
$s=ut-\frac{1}{2}g{t}^2$
$2=100t-5t^2$
$t^2-20t+0.4=0$
$t=\frac{+20\pm \sqrt{400-1.6}}{2}=0.02\text{s}$