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Question
A block of wood of mass 24 kg floats on water. The volume of wood is 0.032 m3. Find:
- the volume of block below the surface of water,
- the density of wood.
(Density of water = 1000 kg m−3)
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Solution
Mass of block of wood = 24 kg
Volume of wood = 0.032 m3
(a) Upthrust = Volume of block below the surface of water (v) × density of liquid × g
Now for floatation , Upthrust = weight of the body = 24 kgf
or , 24 kgf = v × 1000 × g
or , v = `24/1000 = 0.024 "m"^3`
(b) According to the law of floatation,
`"Volume of the submerged block"/"Total volume of block" = "Density of wood"/"Density of water"`
or , `0.024/0.032 = "Density of wood"/1000`
or , Density of wood = `1000 xx 0.024/0.032 = 750 "kgm"^-3`
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