The deformation of a bar under its own weight is different from the deformation when subjected to a direct axial load equal to its own weight. The correct answer is option 'C', which states that the deformation under its own weight is half of the deformation under a direct axial load equal to its own weight. Let's understand why this is the case.

- **Deformation under its own weight**:
When a bar is subjected to its own weight, it experiences a self-weight or its own gravitational force acting downwards. This force creates a compressive stress along the length of the bar. As a result, the bar elongates or stretches under its own weight. This elongation is known as the self-weight deformation.

- **Deformation under a direct axial load equal to its own weight**:
When a bar is subjected to a direct axial load equal to its own weight, an additional load is applied in addition to its self-weight. This additional load creates a greater compressive stress along the length of the bar compared to the self-weight alone. As a result, the bar undergoes more elongation or stretching under this direct axial load.

- **Comparison of deformations**:
Comparing the two scenarios, it is clear that the deformation under a direct axial load equal to its own weight is greater than the self-weight deformation. This is because the direct axial load adds to the self-weight and creates a higher compressive stress in the bar, resulting in more elongation.

- **Mathematical Explanation**:
The deformation of a bar under a direct axial load is given by the formula:
ΔL = (PL) / (AE)
where ΔL is the elongation, P is the applied load, L is the length of the bar, A is the cross-sectional area of the bar, and E is the Young's modulus of the material.

In the case of self-weight deformation, the applied load P is equal to the weight of the bar (W), and the formula becomes:
ΔL_self = (WL) / (AE)

In the case of deformation under a direct axial load equal to its own weight, the applied load P is equal to 2 times the weight of the bar (2W), and the formula becomes:
ΔL_axial = (2WL) / (AE)

Comparing the two formulas, we can see that ΔL_self is half of ΔL_axial, indicating that the deformation under its own weight is half of the deformation under a direct axial load equal to its own weight. Therefore, option 'C' is the correct answer.