Question

A piece of metal weighs 45 g in air and 25 g in a liquid of density $1.5\times {10}^{3}kg-m^{-3}$ kept at 30C.When the temperature of the liquid is raised to 40C, the metal piece weighs 27 g. The density of liquid at 40C is $1.25\times {10}^{3}kg-m^{-3}.$ The coefficient of linear expansion of metal is

• A. $1.3\times {10}^{-3}/C$
• B. $5.2\times {10}^{-3}/C$
• C. $2.6\times {10}^{-3}/C$
• D. $0.26\times {10}^{-3}/C$

Answer 1

The correct option is C $2.6\times {10}^{-3}/C$

The volume of the metal at ${30}^{\circ }C$ is
$V_{30}=\frac{lossofweight}{specificgravity\times g}$
$=\frac{45\times 25g}{1.5\times g}=13.33c{m}^3$
Similarly, volume of metal at ${40}^{\circ }C$
$V_{40}=\frac{40-27g}{1.25\times g}$
$=14.40c{m}^3$
Now, $V_{40}=V_{30}1+\gamma t_2-t_1$
Or $\gamma =\frac{V_{40}-V_{30}}{V_{30}{t}_2-t_1}$
$=\frac{14.40-13.33}{113.334.-30}$
$=8.03\times {10}^{-3}{/}^{\circ }C$
$\therefore$ Coefficient of linear expansion of the metal is
$a=\frac{\gamma }{3}=\frac{8.03\times {10}^3}{3}$
$\approx 2.6\times {10}^3{/}^{\circ }C$