Thin Shell Theory:
In the field of mechanical engineering, the behavior and analysis of thin shells are important topics. A shell is a structural element that is curved or bent in two dimensions, usually with a thickness much smaller than its other dimensions. Thin shells are commonly used in various applications, such as pressure vessels, pipes, and roofs.

Thickness-to-Diameter Ratio:
The thickness-to-diameter ratio is a significant parameter in determining the behavior of a shell. It indicates the relative thickness of the shell wall compared to its diameter. If this ratio is less than one, it implies that the shell is relatively thin.

Interpretation of the Ratio:
To understand why a shell is considered thin when the thickness-to-diameter ratio is less than one, we can consider the geometric and mechanical aspects involved.

Geometric Aspect:
When a shell is thin, the curvature of the shell surface is relatively high compared to its thickness. This means that the shell's shape is primarily defined by its curvature rather than its thickness. As a result, the shell can be approximated as a surface with negligible thickness.

Mechanical Aspect:
When a shell is thin, the distribution of stress and strain across its thickness is significantly different from that of a thick shell. In a thin shell, the majority of the stress is carried by the shell's surfaces, rather than being distributed through its thickness. This behavior is known as membrane action.

Effect on Structural Analysis:
The assumption of thinness allows for simplifications in the analysis of shell structures. The behavior of a thin shell can often be accurately approximated using membrane theory, which neglects the effects of bending and shear deformation. This simplification greatly reduces the complexity of the analysis and allows for more straightforward calculations.

Answer Explanation:
In the given question, the ratio of the thickness of the wall to the diameter of the shell is less than one. According to the interpretation of the thickness-to-diameter ratio, this implies that the shell is relatively thin. Therefore, option C, which states a ratio of 1/20, is the correct answer.

By understanding the concept of thin shells and their behavior, we can determine the appropriate classification of a shell based on its thickness-to-diameter ratio. In this case, the ratio being less than one indicates a thin shell.