Concept:
The effectiveness of a roller depends upon the type of soil being compacted.
Cohesionless soils such as sand and gravel are best compacted by vibration, which rearranges the soil particles into a denser configuration.
Step 1: Understand the suitability of different rollers.
• Sheep foot roller $\rightarrow$ Best for cohesive soils (clay).
• Grid roller $\rightarrow$ Coarse-grained soils with weathered rocks.
• Smooth steel roller $\rightarrow$ Finishing and surface compaction.
• Vibratory roller $\rightarrow$ Best for cohesionless soils.
Step 2: Identify the correct roller.
Since vibration is highly effective for sands and gravels,
\[
\boxed{\text{Vibratory roller is most suitable for cohesionless soils}.}
\]
Therefore, the correct option is
\[
\boxed{(C)\;\text{Vibratory Roller}.}
\]