Question

A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000 kg m⁻³ and density of water = 1000 kg m⁻³.

Answer 1

Given:
Density of iron, ρ_I = 8000 kg/m³ = 8 gm/u
Density of water, ρ_w = 1000 kg/m³ = 1 gm/u
Let x be the external edge of iron.
According to Archemedes' principle,
Weight displaced = Upward thrust
∴ w = u


For the given condition, we have:
Weight of the box = Buoyant force
⇒ V₁${\rho }_I$g = vρ_wg
⇒ (x² × (0.1) × 6) × 8 = x³ × 1 [Volume of iron = v₁ = 6 times the volume of each sheet]
⇒ x = 4.8 cm