Question

A steel bar of cross-section $500$ mm and length $1$ m acted upon by two forces as shown If Young modulus of elasticity of steel is $200\times {10}^9$ $N/m^2$ then elongation of the rod is

• A. $0.05$ mm
• B. $0.5$ mm
• C. $0.1$ mm
• D. $0.2$ mm

Answer 1

Answer: (B)

$0.5$ mm

$\begin{array}{c}\text{Tension in}bar=50\times {10}^{3}N\\ \text{length}=12m\\ {\text{Area of cross section =500mm}}^2\\ Y=200\times {10}^{9}N/m^2\end{array}$

$\begin{array}{cc}\Delta l& =\frac{FL}{AY}\\ & =\frac{{50}^{}\times {10}^3\times 1}{\mathrm{500}\times {10}^6\times 200\times {10}^9}\\ & =\frac{1}{2}\times {10}^{-3}\\ \Delta l& =0.5mm\end{array}$