Properties Of Solids And Liquids Question 550

Question: If two rods of length L and 2L having coefficients of linear expansion $ \alpha $ and $ 2\alpha $ respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composite rod equals :

Options:

A) $ \frac{3}{2}\alpha $

B) $ \frac{5}{2}\alpha $

C) $ \frac{5}{3}\alpha $

D) none of these

Show Answer

Answer:

Correct Answer: C

Solution:

$ (3L){\alpha _{ _{eff}}}\Delta \theta =L\alpha \Delta \theta +2L(2\alpha )(\Delta \theta ) $

$ \therefore $ $ {\alpha _{eff}}=\frac{5}{3}\alpha $



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