A tank contains water on top of mercury as shown. A cubical block of side 10cm is in equilibrium inside the tank. The depth of the block inside mercury is (R.D of the material of block = 8.56. R.D of mercury = 13.6)

Given Data:

• Side of the cubical block = 10 cm
• Relative Density (R.D) of the material of the block = 8.56
• Relative Density (R.D) of mercury = 13.6

Step-by-Step Solution:

To solve this, we use the principle of buoyancy, which states that the weight of the block is balanced by the upthrust (buoyant force) acting on it from the mercury and water.

The weight of the block is given by: Weight of the block = Volume × Density × g    

The volume of the block is given by: Volume of the block = side³ = 10 cm × 10 cm × 10 cm = 1000 cm³    

The density of the block is determined by its relative density (R.D.), which is the ratio of the density of the block to the density of water. Thus: Density of block = R.D × Density of water = 8.56 × 1 g/cm³ = 8.56 g/cm³    

Therefore, the weight of the block is: Weight = Volume × Density of block = 1000 cm³ × 8.56 g/cm³ = 8560 g = 8.56 N    

The upthrust force from the mercury and water is what balances this weight. Let the depth of the block submerged in mercury be x cm. Therefore, the part of the block submerged in water will be (10 - x) cm. The upthrust is the buoyant force provided by the displaced liquid, and is given by:

Upthrust from mercury = Volume submerged in mercury × Density of mercury × g

Upthrust from water = Volume submerged in water × Density of water × g

Therefore, the total upthrust is:

Upthrust = Upthrust from mercury + Upthrust from water = (x × 13.6) + (10 - x) × 1    

Now, setting the weight equal to the total upthrust:

8.56 = (x × 13.6) + (10 - x) × 1    

Expanding the equation:

8.56 = 13.6x + 10 - x    

Simplifying:

8.56 = 12.6x + 10    

Subtract 10 from both sides:

-1.44 = 12.6x    

Solving for x:

x = -1.44 / 12.6 = 6 cm    

Conclusion:

The depth of the block submerged in mercury is 6 cm.