A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external
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.
4 views
1 Answers
Let the required external edge = X cm.
The surface area of the box = 6X² cm²
The volume of the iron in the box =6X²*0.1 cm³ =0.60X² cm³
The mass of iron in the box = (0.60X²/10⁶ m³)*8000 kg/m³
=4.8X²/1000 kg
The volume of the water displaced =X³ cm³
The force of buoyancy
= (X³/10⁶ m³)*1000 kg/m³ =X³/1000 kg
In the given condition weight of the box = the force of buoyancy
→4.8X²/1000 = X³/1000
→X³ = 4.8 X²
→X = 4.8 cm.
4 views
Answered