A closed cubical box is completely filled with water and is accelerated horizontally towards right with an acceleration a. The resultant normal force by the water on the top of the box.

Options

A. passes through the centre of the top
B. passes through a point to the right of the centre
C. passes through a point to the left of the centre
D. becomes zero

Answer

C

Explanation

Consider an element of the liquid of width `dx` and are of cross-section `a'`, at distance `x` from the front of the tank.
Mass of element `dm = pa' dx`
Net force to the right on the element
=`(p + dp)a' - pa' = dp a'`
`a' dp = dm a = pa' = dx a`
`int_B^A dp = rhoa int_0^l dx`
`P_A - P_B = rho al` (l : side of cube)
Consider the top of box
`p = rho ax, dA = l dx`
`dF = p dA = rho al x dx`
Point of application of force from (1) - (1)
`overline x = (int_0^l x dF)/(int_0^l dF) =(int_0^l x^2 dx)/(int_0^l x^l dx) = (|x^3//3|_0^1)/(|x^2//2|_0^l) = (2)/(3) l`.

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