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

 6cm

We need to understand the equilibrium condition for the cubical block. The block is in equilibrium because the total upward force (upthrust) is equal to the downward force (weight of the block). Since the tank contains water on top of mercury, the block experiences two different upthrusts—one from mercury and the other from water.

Given:

• Side of the cubical block = 10 cm
• Relative density (RD) of the material of the block = 8.56
• Relative density (RD) of mercury = 13.6

Step-by-step calculation:

1. The weight of the block can be expressed as:

Weight = Volume × Density × g
Since we are working with relative densities, the formula becomes:
Weight = (Side³) × (Relative Density of the block)
Substituting values:
Weight = 10³ × 8.56 = 856 units

2. The upthrust is the sum of the upthrusts from mercury and water. Upthrust is given by the formula:

Upthrust = Volume submerged × Density of fluid

Here, the block is submerged in both mercury and water. Let the depth of the block inside mercury be x cm. Then, the remaining depth in water is (10 - x) cm.

3. The total upthrust is:

Upthrust = (x × Area × RD of mercury) + [(10 - x) × Area × RD of water]

Simplifying, since Area = Side²:
Upthrust = x × 13.6 + (10 - x) × 1.0

4. Using the equilibrium condition:

Weight = Upthrust

Substituting values:
856 = (x × 13.6) + [(10 - x) × 1.0]

5. Simplify the equation:

856 = 13.6x + 10 - x
856 - 10 = 12.6x
846 = 12.6x
x = 846 / 12.6 = 6 cm

The depth of the block inside mercury is 6 cm.