Question

A rectangular container moves with an acceleration a along the positive direction as shown in figure. The pressure at the point $A$ in excess of the atmospheric pressure $P_0$ is (take $\rho$ as the density of liquid)

• A. $\rho gh$
• B. $\rho al$
• C. $\rho (gh+al)$
• D. Both (a) and (b)

Answer 1

The correct option is D Both (a) and (b)

In such a condition, point A is at a depth $h$ below the water surface.

Thus the pressure at that point is $P_0+\rho gh$

Also this is $l$ distance exists between this point and the rightmost point when it accelerates with $a$ to the right. Thus pressure at this point can be also be said to be $P_0+\rho al$.

These pressures won't add, in fact, they are equal and this is the determining condition for the shape of the liquid in such an acceleration.

Thus $\rho al=\rho gh$

$⟹al=gh$