Question

A liquid stands at the plane level in U-tube when at rest. If areas of cross-section of both the limbs are equal, what will be the difference in heights $h$ of the liquid in the two limbs of U-tube, when the system is given an acceleration $a$ in horizontal direction towards right as shown ?

• A. $\frac{g}{a}\frac{L^2}{H}$
• B. $\frac{La}{g}$
• C. $\frac{L^2}{H}\frac{a}{g}$
• D. $\frac{Lg}{a}$

Answer 1

The correct option is B $\frac{La}{g}$


Due to acceleration in the horizontal direction, the pressure difference between the two extreme points of the horizontal tube$=\rho aL$

Since, this would be compensated by the difference in height,
$h$ of liquid in the two tubes, so

$\rho gh=\rho aL$

$\therefore h=\frac{La}{g}$

Hence, $\left(B\right)$ is the correct answer.

Why this question? Key concept: If a liquid container/ tube is accelerating in a horizontal direction, then the pressure gradient along the horizontal in the direction of acceleration is $\frac{dp}{dx}=-pa$ The negative sign indicates that the pressure increases in a direction opposite to the acceleration in the horizontal direction.