Physics Practice Test: Fluids, Pressure and Buoyancy

Density = mass ÷ volume = 300 ÷ 120 = 2.5 g/cm³. Dividing volume by mass gives 0.40, which would mean the stone floats in water, and it does not.

Pressure = force ÷ area = 600 ÷ 0.020 = 30,000 Pa. Multiplying force by area gives 12, which has the wrong units for pressure.

The extra pressure is ρgh = 1,000 × 9.8 × 5.0 = 49,000 Pa. Leaving out g gives 5,000 Pa, which is not a pressure in pascals.

Pascal’s principle makes the pressure equal on both pistons: 200 ÷ 0.010 = F ÷ 0.50, so F = 20,000 × 0.50 = 10,000 N. Getting 4.0 N comes from flipping the area ratio.

Archimedes’ principle: the buoyant force equals the weight of displaced water, 1,000 × 0.0030 × 9.8 = 29.4 N. The value 3.0 is the mass of the displaced water in kilograms, not a force.

The block is at rest, so the forces on it balance: the water pushes up exactly as hard as gravity pulls down. If the buoyant force were larger, the block would rise further out of the water.

For a floating object, the fraction submerged equals its density divided by the fluid’s density: 0.92 ÷ 1.00 = 92%. The 8% is the part that sticks out above the water.

The continuity equation A₁v₁ = A₂v₂ gives v₂ = 0.040 × 2.0 ÷ 0.010 = 8.0 m/s. A narrower pipe means faster flow, so 0.50 m/s goes the wrong way.

By Bernoulli’s principle, faster-moving air exerts less pressure, so the higher pressure inside the house pushes the roof up. If the outside pressure were higher, the roof would be pressed down instead.

The hull encloses a lot of air, so the ship’s average density is lower than water’s, and it sinks only until the displaced water weighs as much as the ship. A solid steel block of the same mass would sink.