Question

A container is filled to a height of 20 cm with water. A 30 cm thick layer of oil with specific gravity 0.8 floats on the top of water. If the density of water is 1000 kg/m\(^3\) and atmospheric pressure is \(1 \times 10^5\) Pa, then the total pressure at the bottom of the container is:
[Acceleration due to gravity = 10 m/s\(^2\)]

• A. \(1.044 \times 10^5\) Pa
• B. \(1.24 \times 10^5\) Pa
• C. \(1.062 \times 10^5\) Pa
• D. \(1.15 \times 10^5\) Pa

Hint:

Total pressure at a depth in a multi-layer fluid is the sum of atmospheric pressure and hydrostatic pressures of each layer: \(P = P_\text{atm} + \sum_i \rho_i g h_i\).

Answer 1

The Correct Option is A

Step 1: Layered fluid setup.
Water depth h_w = 0.2 m, oil depth h_o = 0.3 m, oil density ρ_o = 0.8 × 1000 = 800 kg/m³, atmospheric pressure P_atm = 1 × 10⁵ Pa.

Step 2: Pressure from water.
P_w = ρ_w g h_w = 1000·10·0.2 = 2000 Pa.

Step 3: Pressure from oil.
P_o = ρ_o g h_o = 800·10·0.3 = 2400 Pa.

Step 4: Total bottom pressure.
P_total = P_atm + P_w + P_o = 1×10⁵ + 2000 + 2400 = 1.044 × 10⁵ Pa.

Step 5: Conclusion.
The absolute pressure at the bottom is 1.044 × 10⁵ Pa.