Properties Of Solids And Liquids Question 499
Question: Two rods, one of aluminum and the other made of steel, having initial length $ l _{1} $ and $ l _{2} $ are connected together to form a single rod of length $ l _{1}+l _{2} $ . The coefficients of linear expansion for aluminum and steel are $ {\alpha _{a}} $ and $ {\alpha _{s}} $ respectively. If the length of each rod increases by the same amount when their temperature are raised by $ t^{o}C $ , then find the ratio $ \frac{l _{1}}{(l _{1}+l _{2})} $ [IIT-JEE (Screening) 2003]
Options:
A) $ \frac{{\alpha _{s}}}{{\alpha _{a}}} $
B) $ \frac{{\alpha _{a}}}{{\alpha _{s}}} $
C) $ \frac{{\alpha _{s}}}{({\alpha _{a}}+{\alpha _{s}})} $
D) $ \frac{{\alpha _{a}}}{({\alpha _{a}}+{\alpha _{s}})} $
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Answer:
Correct Answer: C
Solution:
Given $ \Delta l _{1}=\Delta l _{2} $ or $ l _{1}{\alpha _{a}}t=l _{2}{\alpha _{s}}t $
$ \therefore $ $ \frac{l _{1}}{l _{2}}=\frac{{\alpha _{s}}}{{\alpha _{a}}} $ or $ \frac{l _{1}}{l _{1}+l _{2}}=\frac{{\alpha _{s}}}{{\alpha _{a}}+{\alpha _{s}}} $ .
