Question

A piece of metal weighs 46 g in air. When immersed in a liquid of specific gravity 1.24 at ${27}^0$ it weighs 30g. When the temperature of the liquid is raised to ${42}^0$ in a liquid of specific gravity 1.20, it weighs 30.5g. The coefficient of linear expansion of metal is

• A. $2.23\times {10}^{-5}{/}^{0}C$
• B. $6.7\times {10}^{-5}{/}^{0}C$
• C. $4.46\times {10}^{-5}{/}^{0}C$
• D. none of these

Answer 1

The correct option is A $2.23\times {10}^{-5}{/}^{0}C$

For ${27}^{o}C$ , Loss in weight of the metal $=$ weight of liquid displaced $=46-30=16gm$

Volume of metal at ${27}^{o}C$ is $V_1=\frac{16}{1.24}=12.903c{m}^3$

similarly , volume of metal at ${42}^{o}C$ is $V_1=\frac{46-30.5}{1.20}=12.917c{m}^3$

Volume expansion coefficient of the metal is $\gamma =\frac{V_2-V_1}{V_1({\theta }_2-{\theta }_1)}=\frac{12.927-12.903}{12.903(42-27)}=7.23\times {10}^{-5}{/}^{o}C$

The coefficient of linear expansion of metal is $\alpha =\frac{\gamma }{3}=2.4\times {10}^{-5}{/}^{o}C$