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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/m3 and density of water = 1000 kg/m3.
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Solution
Given:
Density of iron, ρI = 8000 kg/m3 = 8 gm/u
Density of water, ρw = 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 ρIg = vρwg
⇒ (x2 × (0.1) × 6) × 8 = x3 × 1 [Volume of iron = v1 = 6 times the volume of each sheet]
⇒ x = 4.8 cm
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