Waec Model Questions Vol1 2022 Physics Question 7

A frictionless piston seals a fixed‑volume cylindrical container that initially holds 0.020 m³ of air at 300 K and atmospheric pressure (101 kPa). The container is then lowered vertically into a large water tank. The piston is exposed to the water pressure at a depth that can be read on a calibrated scale attached to the container. When the water level above the piston reads 3.5 m, the volume of the trapped air is found to be 0.015 m³ (the temperature of the air remains 300 K). Assume the water temperature is uniform and the acceleration due to gravity is 9.8 m s⁻². Answer the following: a) Determine the absolute pressure of the trapped air at the instant the volume is 0.015 m³. b) Using the result of (a), calculate the density of the water in the tank. c) State the physical principle that justifies the relationship used between the water depth and its pressure.