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Standard VIII

Physics

Floating and Sinking

A uniform sol...

Question

A uniform solid cylinder of density $0.8 g m / c m^{2}$ floats in equilibrium in a combination of two non mixing liquids A and B with its axis vertical.The densities of the liquids A and B are $0.4 g m / c m^{3}$ and $0.7 g m / c m^{3}$ , respectively. The height of liquid A is $h_{A} = 1.2 c m$ .The length of the part of the cylinder immersed in liquid B is $h_{B} = 0.8 c m$
Find h, the length of the part of the cylinder in air.

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Solution

For equilibrium buoyant force= weight of the body
$h_{A} ρ_{A} A g + h_{B} ρ_{B} A g = (h_{A} + h_{A} + h) A ρ_{C} g$
where, $ρ_{C}$ is density of cylinder
$h = [(h_{B} ρ_{A}) + \frac{h_{B} ρ_{B}}{ρ_{C}}] - (h_{A} + h_{B}) = 0.25$

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For equilibrium buoyant force= weight of the body hAρAAg+hBρBAg=(hA+hA+h)AρCgwhere, ρC is density of cylinder h=[(hBρA)+hBρBρC]−(hA+hB)=0.25

For equilibrium buoyant force= weight of the body
$h_{A} ρ_{A} A g + h_{B} ρ_{B} A g = (h_{A} + h_{A} + h) A ρ_{C} g$
where, $ρ_{C}$ is density of cylinder
$h = [(h_{B} ρ_{A}) + \frac{h_{B} ρ_{B}}{ρ_{C}}] - (h_{A} + h_{B}) = 0.25$