Fluids

The total volume of the cube is: The mass of the cube is: The density of the cube is: Since the cube floats, the submerged volume is given by: Thus, the volume outside the water is: Thus, the correct answer is (4) 400 cm³.

Concept: For a small hole in a tank, velocity of efflux is given by Torricelli’s theorem: where is the height of water above the hole. The horizontal range when water falls from height is Step 1: {Find the height of the cylindrical vessel.} Volume of cylinder: Given: Using : Step 2: {Determine vertical heights.} Hole is below the water surface. Thus Height of hole above ground: But vessel is placed on a block of same height : Step 3: {Find the range.}

Concept: According to Archimedes’ principle, the weight of the floating body equals the weight of displaced water. When the coin is placed on the cube, the additional submerged volume corresponds to the weight of the coin.
Step 1:Find additional displaced volume} Base area of cube: Increase in submerged height: Additional displaced volume:
Step 2:Use Archimedes principle} Mass of displaced water equals mass added (coin): Thus

Step 1: Understanding the Concept:
We apply the Principle of Continuity to find the velocity at point B and then use Bernoulli's Equation for a horizontal flow to find the pressure difference.
Step 2: Key Formula or Approach:
1. Continuity: .
2. Bernoulli: .
Step 3: Detailed Explanation:
Convert all units to SI: , Find : Pressure difference :
Step 4: Final Answer:
The difference in pressures is 72 Pa.

Step 1: Apply floating condition.
For a floating body,
Step 2: Substitute given values.

Step 3: Calculate submerged height.