Question

A block of wood of mass 24 kg floats on water. The volume of wood is 0.032 m³. Find: 

1. the volume of block below the surface of water,
2. the density of wood.

(Density of water = 1000 kg m⁻³)

Answer 1

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`