Properties Of Solids And Liquids Question 401
Question: A piece of metal weighs 45g in air and 25g in a liquid of density$ \text{1}\text{.5 }\times\text{ 1}{{\text{0}}^{\text{3}}}\text{kg - }{{\text{m}}^{\text{-3}}} $ kept at$ 3{{0}^{o}}C $ . When the temperature of the liquid is raised to$ 40{}^\circ C, $ , the metal piece weighs 27g. The density of liquid at$ 40{}^\circ C $ , is$ 1.25\times 10^{3}kg -{{m}^{-3}} $ . The coefficient of linear expansion of metal is
Options:
A) $ 1.3\times {{10}^{-3}}/{}^\circ C $
B) $ 5.2\times {{10}^{-3}}/{}^\circ C $
C) $ 2.6\times {{10}^{-3}}/{}^\circ C $
D) $ 0.26\times {{10}^{-3}}/{}^\circ C $
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Answer:
Correct Answer: C
Solution:
[c] $ V _{1}=\frac{4( 5-25 )g}{d _{1}} $ and $ V _{2}=\frac{( 45-27 )g}{d _{2}} $
$ \therefore \frac{V _{1}}{V _{2}}=\frac{20}{18}\times \frac{d _{2}}{d _{1}} $
or $ \frac{V _{1}}{V _{1}( 1+r _{metal}\times 10 )}=\frac{20}{18}\times [ \frac{d _{1}}{( 1+{r _{\ell }}\times 10 )d _{1}} ] $
After simplifying, we get $ \alpha =\frac{{\gamma _{metal}}}{{}}=2.6\times {{10}^{-3}}{{/}^{o}}C $
