A piece of metal weighs 46g times g in air. When immersed in a liquid of relative density 1.24, kept at 27^(@)C, its weight is 30g times g. When the temperature of the liquid is raised to 42^(@)C, the metal piece in it weighs 30.5g times g. At 42^(@)C, the relative density of the liquid is 1.20. Find the coefficient of linear expansion of the metal.

A piece of metal weighs 46g times g in air. When immersed in a liquid

1.	A piece of metal weighs 46g times g in air. When immersed in a liquid of relative density 1.24, kept at 27^(@)C, its weight is 30g times g. When the temperature of the liquid is raised to 42^(@)C, the metal piece in it weighs 30.5g times g. At 42^(@)C, the relative density of the liquid is 1.20. Find the coefficient of linear expansion of the metal.
Answer» Solution :The apparent loss in weight of the metal at `27^(@)C=` weight of an equal VOLUME of the liquid `=(46-39) g times g`, Thus the volume of the displaced liquid at `27^(@)C=(46-30)/1.24=16/1.24 cm^(3)=` volume of the metal piece at `27^(@)C(=V_(1))`. Similarly, the volume of the metal piece at `42^(@)C(=V_(2))=(46-30.5)/(1.20)=15.5/1.20cm^(3)` `THEREFORE` Coefficient of volume expansion of the metal, `gamma=(V_(2)-V_(1))/(V_(1)(t_(2)-t_(1)))=1/((t_(2)-t_(1)))(v_(2)/(v_(1))-1)` `""=1/(42-27)(15.5/1.2 times 1.24/16-1)=1/15(961/960-1)` `therefore` The coefficient of linear expansion of the metal piece, `alpha=gamma/3=(6.94 times 10^(-5))/3""^(@)C^(-1)=23.15 times 10^(-6@)C^(-1).`