According to Euler's column theory, the crippling load for a column of length (l) with one end fixed and the other end hinged can be determined using the formula:

Crippling Load = (2π²EI) / l²

To understand this formula, let's break it down:

**1. Euler's Column Theory:**
Euler's column theory is a fundamental concept in structural engineering that predicts the buckling or crippling load of a slender column under compressive loads. It assumes that the column is perfectly straight, homogeneous, and free from any initial imperfections.

**2. Crippling Load:**
The crippling load is the maximum compressive load that a column can withstand before it buckles or becomes unstable. When the crippling load is exceeded, the column will deflect laterally and lose its ability to support the applied load.

**3. Variables in the Formula:**
- E: Young's modulus of the material
- I: Moment of inertia of the cross-sectional area of the column
- l: Length of the column

**4. Formula Derivation:**
Euler derived the formula for the crippling load of a column based on the equilibrium equation and the assumption that the column deflection is in the form of a sine curve. The derivation involves solving the differential equation governing the column's behavior under axial compression.

**5. Explanation of the Formula:**
The formula for the crippling load (Pc) of a column with one end fixed and the other end hinged is given by:

Pc = (2π²EI) / l²

- The numerator (2π²EI) represents the stiffness of the column. It is directly proportional to the product of Young's modulus (E) and the moment of inertia (I). A higher stiffness indicates that the column is less prone to buckling.
- The denominator (l²) represents the slenderness ratio of the column. It is inversely proportional to the square of the column length (l). A longer column will have a higher slenderness ratio, making it more susceptible to buckling.

**6. Correct Answer:**
Based on the given options, the correct answer is option 'C':

Crippling Load = (2π²EI) / l²

This option matches the formula derived from Euler's column theory, where the slenderness ratio is in the denominator of the formula.