Question

Two cylindrical vessels A and B of different areas of cross-section kept on the same horizontal plane are filled with water to the same height. If the volume of water in vessel A is 3 times the volume of water in vessel B, then the ratio of the pressures at the bottom of the vessels A and B is:

• A. \( 1:1 \)
• B. \( 1:3 \)
• C. \( 1:9 \)
• D. \( 1:6 \)

Hint:

Hydrostatic pressure at a given depth in a fluid depends only on the height of the liquid column and not on the volume or cross-sectional area of the container.

Answer 1

The Correct Option is A

Step 1: Understanding pressure at the bottom of a vessel The pressure at the bottom of a liquid column is given by the hydrostatic pressure formula: \[ P = h \rho g \] where: - \( h \) is the height of the liquid column,
- \( \rho \) is the density of the liquid,
- \( g \) is the acceleration due to gravity.
Step 2: Analyzing given conditions
Since both vessels A and B have water filled to the same height \( h \), and the pressure at the bottom depends only on \( h, \rho, g \), which are the same for both vessels, it follows that: \[ P_A = P_B \] Step 3: Conclusion
Since the pressure at the bottom of both vessels is equal, their ratio is: \[ \frac{P_A}{P_B} = 1:1 \] Thus, the correct answer is option (A) \(1:1\).