Question

What will be the percentage increase in the length of wire, if longitudinal stress of $1kg/m{m}^2$ is applied on it? $\left(Y=10^{11}N/m^2\right)$

• A. $0.002$
• B. $0.001$
• C. $0.003$
• D. $0.01$

Answer 1

Answer: (B)

from hooke's law
Stress $\propto$ Strain
From the question given that stress $=1kg/m{m}^2$
$\Rightarrow 1kg/10^{-6}{m}^2$
$\Rightarrow 10^{6}kg/m^2$
Young's modulus $Y=10^{11}N/m^2$
$\frac{\Delta L}{L}\times 100=?$
Stress $=10^6\times 9.8N/m^2$
$\left[\because \frac{1kg}{m}=1\times 9.8N/m^2\right]$
$\Rightarrow$ Strain $=\frac{\text{Stress}}{Y}$
strain is change in length upon orignal length
$\frac{\Delta L}{L}\Rightarrow \frac{9.8\times 10^6}{10^{11}}$
$\Rightarrow \frac{\Delta L}{L}\times 100=9.8\times 10^{-5}\times 100$
$\Rightarrow 10\times 10^{-5}\times 100$
$\Rightarrow 10^{-2}$
$\left[\because 9.8\simeq 10\right]$
$\frac{\Delta L}{L}\times 100=0.01$