A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are γ1 and γ2respectively. If the temperature of both mercury and metal are increased by an amount ΔT, the fraction of the volume of the metal submerged in mercury changes by the factor

Let f be the fraction of the volume of metal submerged in mercury∴ f= density of metal  density of mercury =ρmetal ρmercury When temperature is increased by Δt, then fraction f'f′=ρmetal 1−γ1Δtρmercury 1−γ2ΔT=f1−γ1ΔT1−γ2ΔT−1=f1+γ2−γ1ΔTFractional change or fraction immersedf′−ff=γ2−γ1ΔT