Question

A truck loaded with a half-filled water tank is moving at a constant horizontal acceleration $a$. The acceleration due to gravity is $g$. At steady state, the angle $\theta$ made by the free surface with the horizontal plane is

• A. $\sin^{-1}(a/g)$
• B. $\tan^{-1}(g/a)$
• C. $\tan^{-1}(a/g)$
• D. $\sin^{-1}(g/a)$

Hint:

Whenever a liquid container accelerates, the free surface tilts such that $\tan\theta$ equals the ratio of horizontal acceleration to gravitational acceleration.

Answer 1

The Correct Option is C

When the truck accelerates horizontally with acceleration $a$, the water inside the tank experiences an inertial force opposite to the direction of motion.
At steady state, the free surface of the liquid aligns perpendicular to the resultant of two accelerations:
1. Horizontal acceleration $a$ of the truck, and
2. Vertical acceleration $g$ due to gravity.
The slope of the free surface is therefore determined by
\[ \tan \theta = \frac{a}{g} \]
Taking the inverse tangent gives
\[ \theta = \tan^{-1}(a/g) \]
Thus, the correct answer is (C).