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Q.

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:

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a

1.01

b

1.03

c

1.04

d

1.26

answer is A.

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

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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: