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A hollow steel ship floats while a steel nail sinks. Both are the same metal, so the material alone cannot be the answer — and the exam knows it. Pressure and floatation is a small chapter with an unusually high question-to-page ratio, because everything in it reduces to three named results you can carry in your head: P = F/A, P = hρg, and Archimedes' principle.
What makes it worth a careful hour is that the questions rarely ask you to calculate. They ask what a quantity depends on. Does liquid pressure depend on the area of the base of the vessel? Does a hydraulic lift multiply work or only force? Does the water level change when floating ice melts? Each has a one-line answer that never varies, and each is printed beside a plausible wrong option. Learn the dependencies, and the arithmetic that remains is a single multiplication.
1. The pressure exerted by a liquid at the bottom of a vessel depends on:
2. In a hydraulic press a force of 100 N is applied on a piston of area 5 cm². What force acts on the larger piston of area 500 cm²?
3. A piece of ice floating in a glass of water melts completely. The level of the water will:
4. A body weighs 50 N in air and 45 N when fully immersed in water. Taking g = 10 m/s² and the density of water as 1000 kg/m³, the volume of the body is:
5. The working of hydraulic brakes in a car is based on:
6. Atmospheric pressure at sea level is equivalent to a mercury column of:
7. When a ship sails from a river into the sea, it:
8. Taking the density of ice as 0.9 g/cm³ and of water as 1.0 g/cm³, the fraction of a floating block of ice that stays above the water surface is: