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

To solve the problem of determining the slope of the free surface of oil in a tanker that is accelerating, we can follow these steps:

### Step 1: Understand the Forces Acting on the Oil
When the tanker accelerates horizontally with an acceleration \( a \), the oil inside experiences a pseudo force acting in the opposite direction of the acceleration. This pseudo force can be represented as \( F_{pseudo} = dm \cdot a \), where \( dm \) is the mass of an elemental volume of oil.

### Step 2: Identify the Weight of the Oil
The weight of the elemental mass of oil is given by \( F_{weight} = dm \cdot g \), where \( g \) is the acceleration due to gravity.

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