B

To analyze the problem, we need to consider how the dimensions of the cylindrical solid change when the temperature varies, due to thermal expansion effects.
1. **Coefficient of Linear Expansion (α)**: This affects the linear dimensions (height and radius) of the cylinder when temperature changes.
2. **Coefficient of Volume Expansion (γ)**: This affects the volume of the liquid when temperature changes.
3. **Floating Condition**: A floating object displaces a volume of liquid equal to its own weight. Therefore, if the volume of the cylinder inside the liquid remains constant, the volume of the liquid displaced must also remain constant irrespective of the temperature change.
4. **Column II Assessment**: For the cylinder to have a constant volume inside the liquid, the expansion of the liquid must balance with the expansion of the solid. This results in the condition where γ = 2α, as the liquid expands in all three dimensions while the cylinder expands in just one dimension when considering height.
Hence, the correct pairing is (b) with (q), leading to the answer being (B).