Question

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

• A. $0.04\text{s}$
• B. $20\text{s}$
• C. $0.4\text{s}$
• D. $0.06\text{s}$

Answer 1

The correct option is B $20\text{s}$

We have,
$\mu =\frac{4.5}{2.25}=2{\text{gm}}^{-1},T=2g=20\text{N}\Rightarrow \text{Velocity,}u=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{20}{2\times {10}^{-3}}}=100{\text{ms}}^{-1}\text{Now, from equation of motion we have}s=ut-\frac{1}{2}g{t}^{2}2=100t-5t^2{t}^2-20t+0.4=0t=\frac{+20\pm \sqrt{400-1.6}}{2}\approx \frac{20\pm \sqrt{400}}{2}=20\text{s}$