Question

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration $2{\text{m/s}}^2$ and a load of $10\text{kg}$ hangs from other end. Area of cross -section of the wire is $2{\text{cm}}^2$. The longitudinal strain in the wire is $(g=10{\text{m/s}}^2$ and $Y=2\times {10}^{11}{\text{Nm}}^{-2})$

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

Answer 1

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

Given that, a load of $10\text{kg}$ hangs in an elevator which is moving up with an acceleration $2{\text{m/s}}^2$
Let $a_0=2{\text{m/s}}^2$
So, tension in the steel wire is given by
$T=m(g+a_0)=10(10+2)=120\text{N}$
Stress in the wire $=\left(\frac{T}{A}\right)=\frac{120}{2\times {10}^{-4}}=60\times {10}^4{\text{Nm}}^{-2}$
and we know that,
$Y=\frac{\text{Logitudinal Stress}}{\text{Longitudinal Strain}}$
$\Rightarrow \text{Longitudinal Strain}=\frac{\text{Longitudinal Stress}}{Y}$
$\Rightarrow \frac{\Delta L}{L}=\frac{60\times {10}^4}{2\times {10}^{11}}$
$=30\times {10}^{-7}\text{or}3\times {10}^{-6}$
Thus, option (b) is the correct answer.