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A wooden block floats in water with two ...

A wooden block floats in water with two third of its volume submerged. A. Calculate the density of wood.b. When the same block is placed in oil, three - quarter of its volume in immersed in oil. Calculate the density of oil.

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Volume of the wooded block = `"V m"^(3) `
Density of the wood = `"d kg m"^(-3)`
Mass of the wooden block = Vd kg
Weight of the wooden block = Vd kgf
Volume under water = `2V//3 "m"^(-3)`
Density of water = `1000 "kg m"^(-3)`
Mass of the displaced water = (2V/3) x 1000 kg
Weight of the displaced water = (2V/3) X 1000 kgf
`therefore` Upthrust = (2V/3) x 1000 kgf
According to law of floatation ,
Weight of the wooden block = Upthrust
Vd=(2V/3) x 1000 kgf
According to law of floatation,
Weight of the wooden block = Upthrust
Vd=(2V/3) x 1000
Or, d=2 x 1000/3
`therefore d=666.67 "kg m"^(3)`
Density of the wooden block = `666.67 "kg m"^(-3)`
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