Question

A steel rod of length $1 \,m$ and radius $10\, mm$ is stretched by a force $100\, kN$ along its length. The stress produced in the rod is $\left(Y_{Steel}=2\times10^{11}N m^{-2}\right)$

• A. $3.18\times10^{6} \,N$ $m^{-2}$
• B. $3.18\times10^{7} \,N$ $m^{-2}$
• C. $3.18\times10^{8} \,N$ $m^{-2}$
• D. $3.18\times10^{9} \,N$ $m^{-2}$

Answer 1

Answer: (C)

Here, $r=10 \,mm$ $=10\times10^{-3}$ $m =10^{-2} \,m$
$L=1 m$, $F=100 \,kN$ $=100\times10^{3} \,N$ $=10^{5} N$
Stress produced in the rod is
Stress $=\frac{F}{A}$ $=\frac{F}{\pi r^{2}}$ $=\frac{100\times10^{3}N}{3.14\times\left(10^{-2}m\right)^{2}}$ $=3.18\times10^{8} \,N$ $m^{-2}$