Properties Of Solids And Liquids Question 414
Question: Coefficient of linear expansion of brass and steel rods are $ {\alpha _{1}} $ and $ {\alpha _{2}} $ . Lengths of brass and steel rods are $ {\ell _{1}} $ and $ {\ell _{2}} $ respectively. If $ ({\ell _{1}}-{\ell _{2}}) $ is maintained same at all temperatures, which one of the following relations holds good?
Options:
A) $ 3{\alpha _{1}}{\ell _{2}}={\alpha _{2}}{\ell _{1}} $
B) $ 4{\alpha _{1}}{\ell _{2}}={\alpha _{2}}{\ell _{1}} $
C) $ 2{\alpha _{1}}{\ell _{2}}={\alpha _{2}}{\ell _{1}} $
D) $ {\alpha _{1}}{\ell _{1}}={\alpha _{2}}{\ell _{2}} $
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Answer:
Correct Answer: D
Solution:
[d] From question, $ ({\ell _{2}}-{\ell _{1}}) $ is maintained same at all temperatures hence changed in length for both rods should be same i.e., $ \Delta {\ell _{1}}=\Delta {\ell _{2}} $ .
As we know, coefficient of linear expansion $ \alpha =\frac{\Delta \ell }{{\ell _{0}}\Delta \ell } $
$ {\ell _{1}}{\alpha _{1}}\Delta T={\ell _{2}}{\alpha _{2}}\Delta T\Rightarrow {\ell _{1}}{\alpha _{1}}={\ell _{2}}{\alpha _{2}} $
