Question

An open square tank of side $1m$ is completely filled with water. If the tank is moved with an acceleration of $10m{s}^2$, find the slope of the free surface of water with the horizontal and the quantity of water which will spill out of the tank.

• A. $1,0.5{\text{m}}^3$
• B. $2,0.5{\text{m}}^3$
• C. $1,0.7{\text{m}}^3$
• D. $3,0.7{\text{m}}^3$

Answer 1

The correct option is A $1,0.5{\text{m}}^3$

As the tank is moving in $+x$ direction and if we consider water as our frame of reference then it will experience acceleration in $-x$ direction as shown and $g$ will be acting in the downward direction.
As we know that pressure line are perpendicular to the resultant acceleration $g_{eff}$.
The slope of the free surface of the water is given by
$\tan \theta =\frac{a}{g}=\frac{10}{10}$
$\tan \theta =1$

As the tank is in square shape and we know $\theta ={\tan }^{-1}1={45}^0$
The volume of the liquid that goes out will be
$V=\frac{1}{2}bht=\frac{1}{2}\times 1\times 1\times 1=0.5m^3$