Question 16 of 192

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

A$1.26$B$1.04$C$1.01$D$1.03$

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Answer: (C) $1.01$

According to Archemedes Principle, weight of the body is balanced by the upward thrust force due to buoyancy.
At $0^{\circ}C$, $mg=A(100-20){\rho }_{0^{\circ}C}g$, where $A$ is area of cross-section of cylinder and ${\rho }_{0^{\circ}C}$ is density of water at $0^{\circ}C$.
At $4^{\circ}C$, $mg=A(100-21){\rho }_{4^{\circ}C}g$, where ${\rho }_{4^{\circ}C}$ is density of water at $4^{\circ}C$.
$\dfrac{{\rho }_{4^{\circ}C}}{{\rho }_{0^{\circ}C}}=\dfrac{80}{79}=1.01$