Question

There is some change in length when a $33000N$ tensile force is applied on a steel rod of area of cross-section ${10}^{-3}{m}^2$. The change of temperature required to produce the same elongation, if the steel rod is heated is (The modulus of elasticity is $3\times {10}^{11}N/m^2$ and the coefficient of linear equation if steel is $1.1\times {10}^{-5}{/}^{o}C$)

• A. ${20}^{o}C$
• B. ${15}^{o}C$
• C. ${10}^{o}C$
• D. $0^{o}C$

Answer 1

The correct option is C ${10}^{o}C$

Elongation due to tensile force $\left(F\right)=\frac{F}{AY}=\frac{33000}{{10}^{-}3\times 3\times {10}^{11}}=1.1\times {10}^{-4}$

Coefficient of linear expansion {$\alpha$} is $1.1\times {10}^{-5}$
Change of temperature dT required to produce the same elongation is given by: $\alpha dT=1.1\times {10}^{-4}$ Hence, $dT={10}^{0}C$