A) material of the rod
B) rise in temperature
C) length of rod
D) none of the above
Correct Answer: C
Solution :
\[{{L}_{t}}={{L}_{0}}(1+\alpha \Delta \theta )\] \[\Delta L={{L}_{t}}-{{L}_{0}}={{L}_{0}}\,\alpha \,\Delta \theta \] ...(i) If the same rod of length Lo is subjected to stress along its length, then extension in length can be calculated by Hooke's law. \[Y=\frac{tress}{strain}=\frac{stress}{\Delta L/{{L}_{0}}}\] \[=\frac{{{L}_{0}}\times stress}{\Delta L}\] \[\therefore \] \[\Delta L=\frac{{{L}_{0}}\times stress}{Y}\] ?.(ii) If the rod is prevented by expanding, we have \[{{L}_{0}}\alpha \,\Delta \theta =\frac{{{L}_{0}}\times stress}{Y}\] \[\therefore \]Stress \[=Y\,\alpha \,\Delta \theta \] (independent of\[{{L}_{0}}\])
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