Final answer:
To find the pressure of the air at the top of the tank, calculate the pressure exerted by each liquid and subtract them from the gauge pressure at the bottom of the tank.
Step-by-step explanation:
To find the pressure of the air at the top of the tank, we need to consider the pressure exerted by each liquid or material in the tank.
The pressure due to the mercury can be calculated using the formula: P = density * g * h, where density is the density of mercury (13,600 kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the mercury column (0.5 m). Similarly, the pressure due to the water can be calculated using the density of water (1,000 kg/m³) and the height of the water column (2 m). The pressure due to the oil can be calculated using the density of oil (600 kg/m³) and the height of the oil column (3 m). Finally, the pressure of the air at the top of the tank can be calculated by subtracting the pressures exerted by the liquids from the gauge pressure at the bottom of the tank.
Therefore:
Pressure of air at the top of the tank = Gauge pressure at the bottom - Pressure due to mercury - Pressure due to water - Pressure due to oil