Question

An air bubble having volume 1 cm³ at depth 40 m inside water comes to the surface. What will be the volume of the bubble at the surface?

• A. 5 cm³
• B. 2 cm³
• C. 4 cm³
• D. 3 cm³

Answer 1

The Correct Option is A

Step 1: Calculate pressures at the surface and depth 

• Pressure at the surface \( P_1 = 10^5 \, \text{Pa}. \)
• Pressure at depth \( P_2 \) is calculated using the formula:
• Substitute \( \rho = 1000 \, \text{kg/m}^3, \, g = 10 \, \text{m/s}^2, \, h = 40 \, \text{m}: \)

Step 2: Apply Boyle’s law

• Given the initial volume \( V_1 = 1 \, \text{cm}^3 \) and constant temperature:
• Substitute \( P_1 = 10^5, \, V_1 = 1 \, \text{cm}^3, \, P_2 = 5 \times 10^5: \)
• Solve for \( V_2 \):

Final Answer:

The volume of the air bubble at depth is \( 5 \, \text{cm}^3. \)