Question

One end of steel wire is fixed to the selling of an elevator moving up with an acceleration $2m/s^2$ and load of 10 kg hangs from other ends area of cross section of the wire is 2 $c{m}^2$. The longitudinal strain in the wire is :

• A. $4\times {10}^{11}$
• B. $2\times {10}^{-6}$
• C. $8\times {10}^{-6}$
• D. $3\times {10}^{-6}$

Answer 1

The correct option is D $3\times {10}^{-6}$

$\begin{array}{c}\text{Acceleration of steel wire}=2m/s^2\\ \text{Load mass = l0kg}\\ \text{Area of aross section}=2{cm}^2=2\times {10}^{-4}{m}^2\end{array}$

$\underset{–}{F\cdot B\cdot D}of\text{load}$

$\begin{array}{cc}T-mg& =ma\\ T& =m(g+a)\\ T& =12mN\end{array}$

$\begin{array}{c}\text{Youngs modulus of steel wire}=2\times {10}^{11}{Nm}^{-2}\\ \text{elongation}△l=\frac{FR}{AY}\\ \Delta l=\frac{(12\times (10\left)\right)\times l}{(2\times {10}^{-4})(2\times {10}^{11})}=3\times {10}^{-6}\end{array}$