A lorry carries a tank of water. If the lorry moves with a uniform acceleration 'a' in the horizontal direction, determine the angle made by the surface of water in the tank with the horizontal.

Explanation

Let the lorry move towards the left. The lorry moving with uniform acceleration a is a non - inertial frame of reference. An observer in this frame considers a pseudo force on the water in tank.

If the lorry moves towards the left as shown in fig. the pseudo force on the water of mass m is ma to the right is represented by `vec(OA)` The gravitational force mg is represented by `vec(OB)` The resultant force is represented by `vec(OC)` For equilibrium, the water surface in the tank must be perpendicular to the resultant `vec(OC)` So, the liquid surface tilts, being raised at the rear. If `theta` is the angle made by the liquid surface with the horizontal,
`tan theta =(BC)/(OB) =a/g` i.e. `theta = tan^(-1) (a//g)`