Sum

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}.

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#### Solution

Given:

Density of iron, ρ_{I} = 8000 kg/m^{3} = 8 gm/u

Density of water, ρ_{w} = 1000 kg/m^{3} = 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

⇒ V_{1 }ρIg = vρ_{w}g

⇒ (x^{2} × (0.1) × 6) × 8 = x^{3} × 1 [Volume of iron = v_{1} = 6 times the volume of each sheet]

⇒ x = 4.8 cm

Concept: Surface Tension

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