Question

Consider an elevator accelerating vertically upwards and a car accelerating on a horizontal road. The pressure in a liquid at two points on the same horizontal plane are equal in which of the situations?

• A. The car only
• B. The elevator only
• C. Both of them
• D. None of them

Answer 1

The correct option is B The elevator only

The pressure difference between any two points in case of an accelerating fluid is,
Along horizontal direction :
$\Delta P=\rho a_x\Delta x...\left(1\right)$
Similarly, along vertical direction :
$\Delta P=\rho a_y\Delta y...\left(2\right)$
where pressure will increase in a direction opposite to that of acceleration.


According to question,
For car (accelerating along horizontal)
$a_x\ne 0$ and $a_y=0$
From Eq.$\left(1\right)$ and $\left(2\right)$,
$\Rightarrow \Delta P\left(\text{horizontal}\right)\ne 0\text{and}\Delta P\left(\text{vertical}\right)=0$
Similarly for elevator,
$a_x=0\text{and}{a}_y\ne 0$
$\Rightarrow \Delta P\left(\text{horizontal}\right)=0\text{and}\Delta P\left(\text{vertical}\right)\ne 0$
Hence, in the case of elevator along horizontal direction,
$\Delta P=0$
Or, $P_1-P_2=0$
$\therefore P_1=P_2$ at two points in a horizontal plane.
Hence, the given statement will be correct in the elevator only.