Two divers G and H are at depths 20m and 40m, respectively below the water surface in a lake. The pressure on…

1. Analyze the question

We are asked to find the ratio of the total pressure at two different depths in a lake. We are given the depths of the divers and the atmospheric pressure expressed in terms of the height of a water column.

2. Explain the concept

The total pressure ($P$) at any depth ($h$) in a liquid is given by the sum of the atmospheric pressure ($P_{atm}$) and the hydrostatic pressure exerted by the liquid column ($P_{liquid} = \rho gh$).

In this problem, the pressure is expressed in terms of the "head" of water (height of water column). Therefore, the formula simplifies to:

Where:

• $P_{atm} = 10\text{ m}$ (given as the equivalent height of water)
• $h$ = depth of the diver

3. Show the solution

Step 1: Calculate the total pressure on diver G ($P_1$)

• Depth of G ($h_1$) = $20\text{ m}$
• $P_1 = P_{atm} + h_1$
• $P_1 = 10\text{ m} + 20\text{ m} = 30\text{ m}$

Step 2: Calculate the total pressure on diver H ($P_2$)

• Depth of H ($h_2$) = $40\text{ m}$
• $P_2 = P_{atm} + h_2$
• $P_2 = 10\text{ m} + 40\text{ m} = 50\text{ m}$

Step 3: Calculate the ratio $P_2 / P_1$

• Ratio = $P_2 / P_1$
• Ratio = $50 / 30$
• Ratio = $5 / 3 \approx 1.666...$

Rounding to two decimal places, we get 1.67.

4. Identify the answer

Comparing our result to the given options, the correct value is 1.67. This matches option C.

5. Tip

Always remember that in physics problems involving pressure in liquids, "total pressure" is the sum of the pressure due to the liquid column plus the atmospheric pressure acting on the surface. Never forget to add the atmospheric pressure, or your ratio will be incorrect!