The free surface of oil in a tanker, at rest, is horizontal if the tanker starts ac celerating the free surface will be titled by an angle `theta.` If the ac celeration is a ` ms^(-2)` what will be the slope of the free surface ?

Explanation

Consider the diagram where a tanker is accelerating with acceleration a.

Consider an elementary particle of the fluid of mass dm.
The acting forces on the particle with respect to the tanker are shown above.
Now, balancing forces (as the particle is in equilibrium along the inclined direction component of weight=component of pseudo force `dmg sin theta=dmacos theta` (we have assumed that the surface is inclined at an angle `theta`) where, dma is pseudo force
`implies g sin theta=acos theta`
`implies a=g tan theta`
`implies tan theta=(a)/(g)=` slope