Question

A breaking stress of a material is ${10}^{6}N/m^2$ If density of material is $3\times {10}^{3}kg/m^3$, what should be the length of the material so that its breaks by it own weight?

• A. 43.3 m
• B. 23.3 m
• C. 13.3 m
• D. 33.3 m

Answer 1

Answer: (D)

33.3 m

$\begin{array}{c}\text{Given that,}\\ \text{Breaking stress of material}={10}^{6}N/m^2\\ \text{density of material}=3\times {10}^{3}kg/m^3\\ \text{Let the length of wire}=l\\ \text{cross section of wire}=A\end{array}$

we know, Breaking Stress $=\frac{F_{\text{Breaking}}}{A}$

$\begin{array}{cc}{F}_{\text{Breaking}}& =\text{Own weight of wire}\\ & =mg\\ & =(P\vee )g\cdot \therefore \rho =\frac{m}{v}\\ \text{Pulting know value in equation(i)}& \end{array}$

$\begin{array}{cc}{10}^6& =\frac{\rho \text{A.l}g}{A}\\ l& =\frac{{10}^6}{\rho g}\\ & =\frac{{10}^6}{3\times {10}^3\times 10}.\\ & =\frac{100}{3}\\ \ell & =33.3\end{array}$