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Grade: 12
        
a cubical boxis to be constructed with iron sheets of 1mm thickness.what can be the the minimum value of external edge so thatcube doesnt sink in water.
density of iron=8000.density of water=1000
 
 
 
 
 
3 months ago

Answers : (2)

Arun
23739 Points
							

 

Let the length of the side of the cube be 'l' meters 
Volume of the cube = L³ 
The area of each face of the cube is L² 
Considering all the 6 faces of the cube, the weight of the cube is  
= 6 × L² × 8000 kg/m³ × 0.001 m  
=  L² × 48 kg/m² 

Weight of the water displaced by the volume of the cube 
=  L³ × 1000 kg/m³ 

Condtion for the block not to sink in water is 
Weight of the cube = Weight of the water displaced by the volume of the cube 
L² × 48 kg/m² = L³ × 1000 kg/m³ 
On solving we get
L =  48 kg/m² / 1000 kg/m³ 
L = 0.048 m 
L = 48 mm
3 months ago
Vikas TU
10364 Points
							
Dear student 
Total surface area of the cube = 6a²
The volume of the iron in the box = 6a² ×  1 × 10⁻³
 = 6 × 10⁻³ a² m³
Now, The mass of iron in the box = Volume × density
=  6 × 10⁻³ a² × 8000
=48a² kg
Weight = 48 × 10 = 480 N.
The volume of the water displaced = a³ cm³  [It will be equal to volume of cube displaced].
∴ Upthrust = a³ × 1000 × 10
= 10⁴a³
Now, 10⁴a³ = 480
a = 48 × 10⁻³ m.
Therefore, a = 4.8 cm.
 
3 months ago
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