A leak proof cylinder of length $$1m$$, made of a metal which has very low coefficient of expansion is floating, vertically in water at $$00C$$ such that its height above the water surface is $$20cm$$. When the temperature of water is increased to $$40C$$, the height of the cylinder above the water surface becomes $$21cm$$. The density of water at $$T=40C$$, relative to the density at $$T=00C$$ is close to:

Question

A leak proof cylinder of length $$1m$$, made of a metal which has very low coefficient of expansion is floating, vertically in water at $$00C$$  such that its height above the water surface is $$20cm$$. When the temperature of water is increased to  $$40C$$, the height of the cylinder above the water surface becomes $$21cm$$. The density of water at  $$T=40C$$, relative to the density at $$T=00C$$ is close to:

Infinity Learn · Accepted Answer

During floating, gravity is balanced by buoyancy​⇒mg $$=$$ B​⇒mg $$=$$ ALρg​⇒At $$0oC$$ , $$mg=A80$$ρ$$00Cg$$   ​⇒At $$4oC$$ , $$mg=A79$$ρ$$40Cg$$     ​Dividing, ρ$$40CP00C=8079=1.01$$

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