Properties Of Solids And Liquids Question 419
Question: A steel rail of length 5 m and area of cross-section $ 40 cm^{2} $ is prevented from expanding along its length while the temperature rises by $ 10{}^\circ C $ . If coefficient of linear expansion and Young’s modulus of steel are $ 1.2\times l{{0}^{-5}} {{K}^{-1}} $ and $ 2\times 10^{11} $
$ {{Nm}^{-2}} $ respectively, the force developed in the rail is approximately:
Options:
A) $ 2\times 10^{7}N $
B) $ 1\times 10^{5}N $
C) $ 2\times 10^{9}N $
D) $ 3\times 1{{0}^{-5}}N $
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Answer:
Correct Answer: B
Solution:
[b] Young’s modulus $ =\frac{Thermalstress}{Stain}=\frac{F/A}{\Delta L/L} $
$ Y=\frac{F}{A.\alpha .\Delta \theta }( \because \frac{\Delta L}{L}\alpha \Delta \theta ) $
Force developed in the rail $ F=Y\alpha \Delta t $
$ =2\times l0^{11}\times 40\times l{{0}^{-4}}\times l.2\times 1{{0}^{-5}}\times 10 $
$ =9.6\times 10^{4}=1\times l0^{5}N $
