Answer: 1350kg/m3
Explanation:
Db = Mb/Vb
900= Mb/Vb
(where Db is the density of the block of wood = 900kg/m3, Mb is its mass and Vb is its volume
Df = Mf/Vf (where Df, Mf and Vf are the density, mass and velocity of the fluid respectively
note that the same mass is involved because the block of wood can only displace its own mass of the fluid
It displaces two-thirds of its own volume in the fluid.
2/3Vf = Vb
Vf = 2Vb/3
Db = Mb/Vb
900 = 2Mb/3Vf
2700Vf = 2Mb
1350Vf = Mb
since Mb = Mf
Df = 1350Vf/Vf
Df= 1350Kg/m3
Answer:
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) = D₁V₁g........................equation 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.
