Question

Find the radius of the wire if the breaking stress of the material of the wire is $2\times {10}^{11}N/m^2.(g=10m/s^2).$

• A. $0.1\times {10}^{-5}m$
• B. $0.3\times {10}^{-5}m$
• C. $0.7\times {10}^{-5}m$
• D. $0.09\times {10}^{-4}m$

Answer 1

The correct option is A $0.1\times {10}^{-5}m$

$\text{Given,}\text{Breaking stress}=2\times {10}^{11}N/m^2$

$\text{Let acceleration is a}$

$\begin{array}{cc}T-3g& =3a-\left(i\right)\\ 4g-T& =4a-\left(ii\right)\\ \text{(i)}+\text{(ii)}& \\ g& =7a\end{array}$

$\begin{array}{c}=\frac{g}{7}\end{array}$

$\text{Now from equation (i)}$

$\begin{array}{cc}T& =3a+3g\\ & =\frac{3g}{7}+3g\\ T& =\frac{24g}{7}\end{array}$

Now

$\begin{array}{cc}\text{stress}& =\frac{T}{\text{Area}}\\ \pi & R^2=\frac{T}{\text{stress}}\\ R& =\sqrt{\frac{T}{\text{stress}\times \pi }}=\sqrt{\frac{\frac{24\times 10}{7}}{2\times {10}^{11}\times 3.14}}\\ R& =0.1\times {10}^{-5}\end{array}$