Question

A steel rod of cross-sectional area 1m2 is acted upon by forces as shown in Fig. Total elongation of the bar is $13\times {10}^{-x}$ m. find the value of x. Take Y=2.0×1011N/m2

Answer 1

We know that the extension due to external force F is given by

$e=\frac{F1}{AY}$ $\therefore e_{AB}=\frac{(60\times {10}^3)\times 1.5}{1\times 2\times {10}^{11}}=4.5\times {10}^{-7}m$

$e_{BC}=\frac{(70\times {10}^3)\times 1}{1\times 2\times {10}^{11}}=3.5\times {10}^{-7}m$ and

$e_{CD}=\frac{(50\times {10}^3)\times 2}{1\times 2\times {10}^{11}}=5.0\times {10}^{-7}m$

The total extension $e=e_{AB}+e_{BC}+e_{CD}$

$e=4.5\times {10}^{-7}+3.5\times {10}^{-7}+5.0\times {10}^{-7}$

Hence $x=7$