Question

The breaking stress of aluminium is $7.5\times {10}^{7}N{m}^{-2}$. The greatest length of aluminium wire that can hang vertically without breaking is(Density of auminium is $2.7\times {10}^{3}kg{m}^{-3}$)

• A. $283\times {10}^{3}m$
• B. $28.3\times {10}^{3}m$
• C. $2.83\times {10}^{3}m$
• D. $0.283\times {10}^{3}m$

Answer 1

Answer: (C)

$2.83\times {10}^{3}m$

$\begin{array}{c}\text{Given, breaking stress of aluminium}=7.5\times {10}^{7}N/m^2\\ \text{Density of aluminium}==2.7\times {10}^{3}kg/m^3\\ \text{Stress}=\frac{F}{A}=\frac{mg}{A}\\ d=\frac{m}{A\times L}\Rightarrow \frac{m}{A}=dxL\\ \therefore 7.5\times {10}^{73}=2\cdot 7\times {10}^3\times L\times 100\\ L=2.83\times {10}^{3}m\text{.}\end{array}$