A bucket resting on the floor of an elevator contains an incompressible fluid of density .When the elevator has a downward acceleration of magnitude a the pressure difference between two points in a fluid, separated by a vertical distance $\Delta$ h, is given by:
A)" a$\Delta$h"
B)" g$\Delta$h"
C)" (g + a)$\Delta$h"
D)" (g - a)$\Delta$h"
E)" ga$\Delta$h"

Question

A bucket resting on the floor of an elevator contains an incompressible fluid of density   .When the elevator has a downward acceleration of magnitude a the pressure difference between two points in a fluid, separated by a vertical distance  $\Delta$ h, is given by:
A)" a$\Delta$h" 
B)" g$\Delta$h" 
C)" (g + a)$\Delta$h" 
D)" (g - a)$\Delta$h" 
E)" ga$\Delta$h"

Quizplus · Accepted Answer

The correct formula for the pressure difference in a fluid due to acceleration is $\rho(g - a)\Delta h$, where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, $a$ is the acceleration of the elevator, and $\Delta h$ is the vertical distance between two points in the fluid. Since the elevator is accelerating downwards, the effective acceleration acting on the fluid is $g - a$.

A Bucket Resting on the Floor of an Elevator Contains Δ\DeltaΔ

A Bucket Resting on the Floor of an Elevator Contains $\Delta$