Question

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

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

Answer 1

Answer: (B)

Here$T=m\left(g+a_0\right)=10(10+2)=120N$
$\therefore$ Stress $=\frac{T}{A}$
$=\frac{120}{2\times 10^{-4}}=60\times 10^{4}N{m}^{-2}$
and $Y=\frac{\text{ stress }}{\text{ strain }}$
$\therefore \text{ strain }=\frac{\text{ stress }}{Y}$
$=\frac{60\times 10^4}{2\times 10^{11}}=30\times 10^{-7}=3\times 10^{-6}$