Question

A liquid of density \( d \) is moving down in a vessel of height \( h \) with an acceleration \( a<g \). Then the pressure at the bottom is?

• A. \( hdg \)
• B. \( hd(g - a) \)
• C. \( hd(g + a) \)
• D. \( \frac{hdg}{a} \)

Hint:

When a liquid is moving, the effective acceleration is reduced by the motion, and the pressure at the bottom is calculated with \( g - a \) instead of \( g \).

Answer 1

The Correct Option is B

The pressure at the bottom of the liquid column is given by the hydrostatic pressure formula: \[ P = \rho gh \] Where \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the height of the liquid column.

1. Step 1: Adjust for acceleration. When the liquid is moving with acceleration \( a \), the effective acceleration contributing to the pressure is \( g - a \), because the liquid is not experiencing the full gravitational acceleration due to its motion.

2. Step 2: Calculate the pressure. The pressure at the bottom is therefore: \[ P = \rho h (g - a) \] Substituting \( \rho = d \) (the density of the liquid), the pressure becomes: \[ P = hd(g - a) \] Thus, the correct answer is \( hd(g - a) \).