Question

A load of $1$ kg weight is attached to one end of a steel wire if cross sectional area $3m{m}^2$ mm and young's modulus ${10}^{11}N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontal and released. when the load passes through its lowest position the fractional change in length is $\left(g=10m/s^2\right)$

• A. ${10}^{-4}$
• B. ${10}^{-3}$
• C. ${10}^3$
• D. ${10}^4$

Answer 1

The correct option is A ${10}^{-4}$

$\begin{array}{c}\text{Velocity of load on reaching}B=\sqrt{2gL}\\ \text{Tension at}B=mg+\frac{m{\nu }^2}{L}=3mg\\ \frac{\Delta L}{L}=\frac{F}{YA}=\frac{3mg}{AY}\end{array}$

$\begin{array}{c}=\frac{3\times 1\times 10}{{10}^{11}\times 3\times {10}^{-6}}\\ \frac{\Delta L}{L}={10}^{-4}\end{array}$