Question

Three identical vessels are filled up to the same height with three different liquids A, B, and C of densities \( \rho_A \), \( \rho_B \), and \( \rho_C \) respectively. If \( \rho_A >\rho_B >\rho_C \), then the pressure at the bottom of the vessels is?

• A. equal in all vessels
• B. maximum in a vessel containing liquid C
• C. maximum in vessel containing liquid B
• D. maximum in vessel containing liquid A

Hint:

In hydrostatics, the pressure at the bottom of a liquid column depends on the density of the liquid and the height of the column. A denser liquid results in higher pressure at the bottom.

Answer 1

The Correct Option is D

Step 1: Formula for pressure at the bottom of a liquid column 
The pressure at the bottom of a liquid column is given by the hydrostatic pressure formula: \[ P = P_0 + \rho g h \] where: - \( P_0 \) is the atmospheric pressure (same for all vessels), - \( \rho \) is the density of the liquid, - \( g \) is the acceleration due to gravity, - \( h \) is the height of the liquid column. Since all vessels are filled to the same height \( h \) and are open to the atmosphere, the pressure difference at the bottom of each vessel is: \[ P_{\text{bottom}} = \rho g h \] 

Step 2: Compare pressures for different liquids 
Since \( \rho_A>\rho_B>\rho_C \), it follows that: \[ P_A>P_B>P_C \] 

Step 3: Determine which vessel has a maximum pressure 
From the relation \( P_A>P_B>P_C \), it is clear that the vessel containing liquid A has the maximum pressure at the bottom. Thus, the correct answer is that the pressure is 

maximum in the vessel containing liquid A.