Arectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm. when the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. what is the density of the wood?

825 kgm⁻³

Explanation:

ρ = density of wood = ?

ρ' = density of water = 1000 kgm⁻³

V = volume of wood = 10 x 4 x 2 = 80 cm³ = 80 x 10⁻⁶ m³

V' = Volume of water displaced = 10 x 4 x 1.65 = 66 cm³ = 66 x 10⁻⁶ m³

Using equilibrium of force in vertical direction

Force of buoyancy = Weight of the wood

ρ' V' g = ρ V g

ρ' V' = ρ V  

(1000) (66 x 10⁻⁶) = ρ (80 x 10⁻⁶)

ρ = 825 kgm⁻³