The energy absorbing capacity of a part subject to dynamic forces is determined by various factors. In this case, we are given that the Young's modulus of elasticity (E) remains constant. Let's understand why the correct answer is option 'C' - volume.

Young's modulus of elasticity (E) is a measure of the stiffness or rigidity of a material. It quantifies the relationship between stress and strain in a material. When E remains constant, it means that the material's ability to deform under load does not change. However, the energy absorbing capacity of a part subject to dynamic forces depends on more than just the material's stiffness.

Here's a detailed explanation of why the energy absorbing capacity is a function of volume:

1. Definition of energy absorbing capacity:
- Energy absorbing capacity refers to the ability of a material or a structure to absorb and dissipate energy when subjected to dynamic loads or impacts.
- It is important in applications where impact resistance or shock absorption is required, such as in automotive crash structures, sports equipment, or building structures in earthquake-prone areas.

2. Length (option 'A'):
- The length of a part does not directly affect its energy absorbing capacity.
- Length may indirectly influence the energy absorption capability through the geometry or shape of the part, but it is not a direct factor.

3. Cross-section (option 'B'):
- The cross-sectional area of a part can affect its energy absorbing capacity.
- A larger cross-sectional area generally allows for more material to be deformed or crushed, resulting in higher energy absorption.
- However, when the Young's modulus remains constant, the effect of cross-section on energy absorption is not significant on its own. It is more relevant when comparing parts made of different materials.

4. Volume (option 'C'):
- The volume of a part directly affects its energy absorbing capacity.
- A larger volume means more material is available to absorb and dissipate energy.
- When subjected to dynamic forces, a part with a larger volume can deform or crush over a greater distance, resulting in higher energy absorption.

Therefore, the energy absorbing capacity of a part subject to dynamic forces is primarily determined by its volume. While factors such as length and cross-section may have some influence, they are not as critical as volume when the Young's modulus of elasticity remains constant.