First slide

Pressure in a fluid-mechanical properties of fluids

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 $0^{0} C$ such that its height above the water surface is 20cm. When the temperature of water is increased to $4^{0} C$ , the height of the cylinder above the water surface becomes 21cm. The density of water at $T = 4^{0} C$ , relative to the density at $T = 0^{0} C$ is close to:

Moderate

A

1.01
B

1.03
C

1.04
D

1.26

Solution

$\begin{array}{l} D u r i n g f l o a t i n g, g r a v i t y i s b a l a n c e d b y b u o y a n c y \\ \Rightarrow m g = B \\ \Rightarrow m g = A L ρ g \\ \Rightarrow A t 0^{o} C, m g = A (80) ρ_{0^{0} C} g \\ \Rightarrow A t 4^{o} C, m g = A (79) ρ_{4^{0} C} g \\ D i v i d i n g, \\ \frac{ρ_{4^{0} C}}{P_{0^{0} C}} = \frac{80}{79} = 1.01 \end{array}$

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