Ablock of wood has a density of 900 kg/m3 . it is placed in a fluid in which it floats with two-thirds of its volume submerged. what is the density of the fluid? express your answer in kilograms per cubic meter to three significant figures.

The density of the fluid = 1350 kg/m³.

Explanation:

According to law of floatation,

The weight of fluid displayed is equal to the weight of block wood.

Weight of block wood (W₁) = D₁V₁gequation 1a

Where D₁ = density of the block, V₁= volume of the block, g = acceleration due to gravity.

Weight of the displaced fluid (W₂) = D₂V₂g equation 1b

Where D₂ = density of the displaced fluid, V₂ = Volume of the displaced fluid and g = acceleration due to gravity.

Since W₁ = W₂ ( from law of floatation)

∴   D₁V₁g = D₂V₂g Equation 2

But The volume of the block submerged = 2/3V₁

From Archimedes principle,

the volume of subject immersed in water = the volume of the displaced fluid.

 V₂ = 2/3V₁

Substituting this value into equation 2

D₁V₁g =  D₂2/3V₁g 3

Simplifying  equation 3,

Therefore, D₂ = 3/2(D₁) Equation 4

where D₁ = 900 kg/m³

 D₂ = 3/2(900)

 D₂ = 1350 kg/m³.

The density of the fluid = 1350 kg/m³.

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