A leak proof cylinder of length 1 m , made of a metal which has very low coefficient of expansion is floating vertically in water at 0 o C such that its height above the water surface is 20 c m . When

Question

A leak proof cylinder of length 1 m , made of a metal which has very low coefficient of expansion is floating vertically in water at 0 o C such that its height above the water surface is 20 c m . When the temperature of water is increased to 4 o C , the height of the cylinder above the water surface becomes 21 c m . The density of water at T = 4 o C , relative to the density at T = 0 o C is close to:

TestHub · Accepted Answer

According to Archemedes Principle, weight of the body is balanced by the upward thrust force due to buoyancy.

At $0 ° C$ , $m g = A (100 - 20) ρ_{0 ° C} g$ , where $A$ is area of cross-section of cylinder and $ρ_{0 ° C}$ is density of water at $0 ° C$ .
At $4 ° C$ , $m g = A (100 - 21) ρ_{4 ° C} g$ , where $ρ_{4 ° C}$ is density of water at $4 ° C$ .
$\frac{ρ_{4 ° C}}{ρ_{0 ° C}} = \frac{80}{79} = 1.01$

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