What will be the pressure on a swimmer 10 m below the surface of a lake ?

Question

Accepted Answer

To determine the pressure on a swimmer 10 meters below the surface of a lake, we need to consider both the atmospheric pressure at the surface and the pressure due to the water column above the swimmer.

1. **Explanation for Option 2 (2 atm):**

- **Atmospheric Pressure:** At the surface of the lake, the atmospheric pressure is approximately 1 atm (atmosphere).
   - **Water Pressure:** The pressure due to the water column can be calculated using the formula:
     $$
     P = \rho \cdot g \cdot h
     $$
     where $ \rho $ is the density of water (approximately $ 1000 \, \text{kg/m}^3 $), $ g $ is the acceleration due to gravity (approximately $ 9.81 \, \text{m/s}^2 $), and $ h $ is the depth (10 meters in this case).
     $$
     P = 1000 \, \text{kg/m}^3 \cdot 9.81 \, \text{m/s}^2 \cdot 10 \, \text{m} = 98100 \, \text{Pa} = 0.981 \, \text{atm}
     $$
   - **Total Pressure:** The total pressure on the swimmer is the sum of the atmospheric pressure and the water pressure:
     $$
     \text{Total Pressure} = 1 \, \text{atm} + 0.981 \, \text{atm} \approx 2 \, \text{atm}
     $$
   Therefore, the pressure on the swimmer 10 meters below the surface is approximately 2 atm, which supports Option 2 as the correct answer.

2. **Explanation for why other options are incorrect:**

- **Option 1 (1 atm):** This option is incorrect because it only accounts for the atmospheric pressure at the surface and does not include the additional pressure from the water column. At 10 meters depth, the water pressure contributes significantly to the total pressure, making it greater than 1 atm.

- **Option 3 (5 atm):** This option is incorrect because it overestimates the pressure at 10 meters depth. The calculation shows that the pressure due to the water column is approximately 0.981 atm, and when added to the atmospheric pressure, the total is around 2 atm, not 5 atm.

- **Option 4 (10 atm):** This option is incorrect as it greatly overestimates the pressure. A pressure of 10 atm would imply a much greater depth than 10 meters. The calculation clearly shows that the total pressure at 10 meters is approximately 2 atm.

In conclusion, based on the calculations and logical reasoning, Option 2 (2 atm) is the correct answer for the pressure on a swimmer 10 meters below the surface of a lake.