Question:

A rectangular truck tank $1\mathrm{.}5$ m wide, $3$ m long, and $1\mathrm{.}8$ m deep contains water to a depth of $1\mathrm{.}2$ m $.$ Find the horizontal accelerations which may be imported to the tank in the direction of its length so that $($a$)$ there is just no spilling of water from the tank $($see Fig$\mathrm{.}1-$A$),($b$)$ the front bottom corner of the tank is just exposed $($see Fig$\mathrm{.}1-$B$),($c$)$ the bottom of the tank is exposed upto its mid$-$point $($see Fig$\mathrm{.}1-$C$).$ Calculate the volume of water that would spill out from the tank in the cases $($b$)$ and $($c$).$ Also, calculate the total forces on each end of the tank in each of these cases and show that the differences between these forces equals the unbalanced force necessary to accelerate the liquid mass in the tank. Take the densities of water is $1000k\frac{g}{m^3}.$