The deepest known point on Earth is called the Mariana Trench, at ~11,000 m (~36,000 ft). If the surface area of the average human ear is 20 cm2, how much average force would be exerted on your ear at that depth?

• A. 2.22×10⁵ N
• B. 2.22×10⁷ N
• C. 1.11×10⁸ N
• D. 2.22×10⁹ N

Answer: (A)

Verified step by step guidance

1. First, understand that the force exerted on an object submerged in a fluid is due to the pressure at that depth. The pressure at a certain depth in a fluid is given by the formula: \( P = P_0 + \rho g h \), where \( P_0 \) is the atmospheric pressure at the surface, \( \rho \) is the density of the fluid (for seawater, approximately 1025 kg/m³), \( g \) is the acceleration due to gravity (approximately 9.81 m/s²), and \( h \) is the depth (11,000 m in this case).
2. Calculate the pressure at the depth of the Mariana Trench. Assume \( P_0 \) (atmospheric pressure) is approximately 101,325 Pa (Pascals). Substitute the values into the pressure formula: \( P = 101325 + 1025 \times 9.81 \times 11000 \).
3. Once you have the pressure, calculate the force exerted on the ear using the formula: \( F = P \times A \), where \( A \) is the area of the ear. Convert the area from cm² to m²: 20 cm² = 0.002 m².
4. Substitute the calculated pressure and the area into the force formula: \( F = P \times 0.002 \).
5. Evaluate the expression to find the force. Compare your result with the given options to determine the correct answer.