4. A cylindrical jar of cross-sectional area of 50 cm² is filled with water to a height of 20 cm. It carries a tight fitting piston of negligible mass. Calculate the pressure at the bottom of the jar when a mass of 1 kg is placed on the piston. Ignore atmospheric

To calculate the pressure at the bottom of the jar, we need to consider both the pressure due to the water and the pressure due to the mass placed on the piston.

1. First, calculate the pressure due to the water. The formula for pressure is P = hρg, where h is the height of the water, ρ is the density of the water, and g is the acceleration due to gravity.

   Given that h = 20 cm = 0.2 m (since 1 m = 100 cm), ρ = 1000 kg/m³ (the density of water), and g = 9.8 m/s² (the acceleration due to gravity), we can substitute these values into the formula to get:

   P_water = 0.2 m * 1000 kg/m³ * 9.8 m/s² = 1960 Pa (Pascal is the SI unit of pressure)

2. Next, calculate the pressure due to the mass placed on the piston. The formula for pressure is P = F/A, where F is the force and A is the area.

   The force F is equal to the mass m times the acceleration due to gravity g, so F = mg. Given that m = 1 kg and g = 9.8 m/s², we get F = 1 kg * 9.8 m/s² = 9.8 N (Newton is the SI unit of force).

   The area A is given as 50 cm² = 0.005 m² (since 1 m² = 10,000 cm²), so we can substitute the values of F and A into the formula to get:

   P_mass = 9.8 N / 0.005 m² = 1960 Pa

3. Finally, add the pressures due to the water and the mass to get the total pressure at the bottom of the jar:

   P_total = P_water + P_mass = 1960 Pa + 1960 Pa = 3920 Pa

So, the pressure at the bottom of the jar when a mass of 1 kg is placed on the piston is 3920 Pa.