Question

A racing car has a fuel tank which is partially filled. The car gets into motion in the horizontal direction at a uniform acceleration equal to 'g'. The free surface of the liquid fuel in the tank will assume a slope (with the horizontal) of:
1. 20° 
2. 30° 
3. 45° 
4. 60° 
5.

Answer 1

Correct Answer - Option 3 : 45° 

Concept:

In a liquid container subjected to a constant acceleration a, having components a_x and a_y, the slope of the surface of constant pressure is given by,

\(\frac{{dz}}{{dx}} = - \frac{{{a_x}}}{{g + {a_z}}}\)

For constant horizontal acceleration a, the slope of the constant pressure is

\(\tan θ = \frac{{dz}}{{dx}} = - \frac{a}{g}\)

For constant vertical acceleration, the surface of constant pressure are horizontal

\(\tan θ = \frac{{dz}}{{dx}} = 0\)

Explanation:

given,

Horizontal acceleration, a_x = g

For constant horizontal acceleration a, the slope of the constant pressure is

\(\tan θ = \frac{{dz}}{{dx}} = - \frac{a}{g}\)

tanθ = g/g = 1

θ = 45°