A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :
Solution
In both cases weight of the cylinder is balanced by buoyant force exerted by liquid.
<br><br>Case - 1 : ${\rho _{0^\circ C}}\left( {100 - 20} \right) \times g$ = mg
<br><br>Case - 2 : ${\rho _{4^\circ C}}\left( {100 - 21} \right) \times g$ = mg
<br><br>$\therefore$ $${{{\rho _{4^\circ C}}\left( {100 - 21} \right)} \over {{\rho _{0^\circ C}}\left( {100 - 20} \right)}}$$ =1
<br><br>$\Rightarrow$ ${{{\rho _{4^\circ C}}} \over {{\rho _{0^\circ C}}}}$ = ${{80} \over {79}}$ = 1.01
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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