A solid is floating in a liquid with some fraction of its volume submerged. If for two different temperatures T 1 and T 2 , the fractions of the volume of the solid submerged in the liquid are f 1 and f 2 respectively, then the coefficient of volume expansion of the liquid is [Assume that the expansion of the solid is negligible]

Step-by-step solution

Let V be the volume of solid ; d be its density and m be its mass; if γ is the coefficient of volume expansion of the liquid, then Density at temperature t 1 i s , d 1 = d 0 1 + γ t 1 Density at temperature t 2 i s , d 2 = d 0 1 + γ t 2 According to Archimede's principle, f 1 V d 1 = m = f 2 V d 2 Or d 1 d 2 = f 2 f 1 = d 0 1 + γ t 1 1 + γ t 2 d 0 Or f 1 + f 1 γ t 2 = f 2 + f 2 γ t 1 f 1 - f 2 = γ f 2 t 1 - f 1 t 2 γ = ( f 1 - f 2 ) f 2 t 1 - f 1 t 2