Explanation:

Compression members with double angle sections:
- A compression member is a structural element designed to carry compressive loads.
- A double angle section refers to a structural shape made up of two angles connected back-to-back.

Minimum radius of gyration:
- The minimum radius of gyration is a measure of the efficiency of a structural section in resisting bending and buckling.
- It is denoted by the symbol 'r' and represents the distance from the centroid of the section to an axis parallel to the centroidal axis, at which the moment of inertia is minimum.

Comparison of different double angle sections:
a) Equal angles back-to-back:
- In this configuration, two equal angles are connected back-to-back to form the section.
- Since the angles are equal, the distance of the centroid from the axis passing through the centroid and parallel to the centroidal axis will be equal for both angles.
- Therefore, the centroidal axis will pass through the centroid of each angle.
- As a result, the minimum radius of gyration will be relatively smaller compared to other configurations.

b) Unequal angle with long legs back-to-back:
- In this configuration, two unequal angles with long legs are connected back-to-back to form the section.
- The centroid of each angle will be located closer to the longer leg.
- Hence, the centroid of the composite section will also be closer to the longer leg.
- As a result, the distance of the centroid from the axis passing through the centroid and parallel to the centroidal axis will be larger for the section.
- Therefore, the minimum radius of gyration will be relatively larger compared to the equal angle configuration.

c) Unequal angles with short legs back-to-back:
- In this configuration, two unequal angles with short legs are connected back-to-back to form the section.
- Similar to the previous case, the centroid of each angle will be located closer to the longer leg.
- However, in this configuration, the distance of the centroid from the axis passing through the centroid and parallel to the centroidal axis will be smaller compared to the unequal angle configuration with long legs.
- Therefore, the minimum radius of gyration will be relatively smaller than the unequal angle configuration with long legs.

d) None of the above:
- This option is incorrect as the previous explanation showed that the unequal angle configuration with long legs back-to-back gives a larger value of the minimum radius of gyration compared to the other configurations.

Therefore, the correct answer is option 'B' - Unequal angle with long legs back-to-back.