C

To find the dimensional formula for root mean square (RMS) velocity, we start by considering the formula for velocity, which is defined as displacement over time. The dimensional formula for displacement is [L] (length) and for time is [T]. Therefore, the dimensional formula for velocity (v) is given by:
\[ [v] = \frac{[L]}{[T]} = [L][T]^{-1} \]
The root mean square velocity is defined mathematically as \( v_{rms} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} v_i^2} \). The root mean square does not change the dimensional analysis since it only involves averaging and taking a square root, which does not add or remove dimensions.
Hence, the dimensional formula for root mean square velocity remains the same as that for velocity: \[ [v_{rms}] = [L][T]^{-1} \] This matches with the option C provided in the images.