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Density

When a cube o...

Question

When a cube of wood floats in water, 60% of its vol. is submerged. When the same cube floats in an unknown liquid 85% of its volume is submerged. Find the density of the wood and the liquid?

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Solution

Condition to float:

Weight of the cube = Weight of the liquid displaced by immersed portion

Case I:

Weight of wooden cube = Weight of water displaced by immersed portion

$ρ_{w o o d} V g = ρ_{w a t e r} (0.6 V) g ρ_{w o o d} = 0.6 ρ_{w a t e r} = 0.6 (1 g / c c) = 0.6 g / cc$

Case II:

Weight of wooden cube = Weight of liquid displaced by immersed portion

$ρ_{w o o d} V g = ρ_{l i q u i d} (0.8 V) g ρ_{w o o d} = 0.8 ρ_{l i q u i d} ρ_{l i q u i d} = \frac{ρ_{w o o d}}{0.8} = \frac{0.6}{0.8} = 0.75 g / cc$

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