A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are γ$$1$$ and γ$$2respectively$$. 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

Question

A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are γ$$1$$ and γ$$2respectively$$. 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

Infinity Learn · Accepted Answer

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 $$1$$−γ$$1$$Δtρmercury $$1$$−γ$$2$$Δ$$T=f1$$−γ$$1$$Δ$$T1$$−γ$$2$$ΔT−$$1=f1+$$γ$$2$$−γ$$1$$ΔTFractional change or fraction immersedf′−$$ff=$$γ$$2$$−γ$$1$$ΔT

A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are $γ_{1} and γ_{2}$ respectively. 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

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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

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A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are $γ_{1} and γ_{2}$ respectively. 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