A closed cubical box is entirely filled with water and undergoes a...

When the box accelerates horizontally to the right with acceleration $a$, a pseudo force acts on the water towards the left.

The pressure gradient in the horizontal direction is given by $\dfrac{dP}{dx} = -\rho a$, where $\rho$ is the density of water and $x$ is the distance measured from the left face towards the right.

This shows that the pressure decreases linearly from left to right. Therefore, the pressure on the top surface is maximum at the left edge and minimum at the right edge.

The normal force exerted by the water on an elemental area of the top surface is proportional to the pressure at that point. Since the pressure is higher on the left half of the top surface compared to the right half, the distribution of force is skewed towards the left.

Consequently, the point of application of the resultant normal force (centre of pressure) will shift towards the region of higher pressure, which is to the left of the geometric centre of the top surface.