The slenderness ratio is a term used to describe the stability and strength of a column. It is defined as the ratio of the equivalent length of the column to the minimum radius of gyration. The correct answer is option 'A', which states that the slenderness ratio is the ratio of the equivalent length of the column to the minimum radius of gyration.

Explanation:
1. Slenderness ratio definition: The slenderness ratio (λ) is a measure of the column's ability to resist buckling under a compressive load. It is calculated by dividing the effective length of the column by the minimum radius of gyration.
2. Equivalent length of the column: The equivalent length of a column is the length of an idealized column that would have the same buckling behavior as the actual column. It takes into account the end conditions and the support conditions of the column.
3. Minimum radius of gyration: The minimum radius of gyration (r) is a geometric property of the cross-section of the column. It represents the smallest radius at which the mass of the cross-section could be concentrated without changing the resistance to buckling.
4. Importance of slenderness ratio: The slenderness ratio is an important parameter in the design of columns because it determines the critical load at which the column will buckle. Columns with higher slenderness ratios are more prone to buckling and require greater design considerations.
5. Buckling of columns: When a column is subjected to a compressive load, it may buckle or fail due to insufficient stability. Buckling occurs when the compressive load exceeds the critical buckling load, which is determined by the slenderness ratio.
6. Design considerations: In structural design, the slenderness ratio is used to determine the appropriate column dimensions and materials. For columns with low slenderness ratios, such as short and stocky columns, the design can focus on material strength. However, for columns with high slenderness ratios, such as long and slender columns, additional measures may be necessary to increase stability, such as bracing or increasing the column's cross-sectional area.
7. Limitations: It is important to note that the slenderness ratio is applicable for slender columns subjected to axial compression loads. It may not be suitable for columns subjected to other types of loads, such as bending or torsion.
8. Conclusion: In summary, the slenderness ratio is the ratio of the equivalent length of the column to the minimum radius of gyration. It is a crucial parameter in the design of columns, as it determines the critical buckling load and helps in selecting appropriate dimensions and materials for the column to ensure stability and strength.