The root mean square velocity of molecules of gas is

We need to determine the dependence of root mean square (RMS) velocity of gas molecules on temperature.

Write the formula for RMS velocity.

$$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$

where $$R$$ is the universal gas constant, $$T$$ is the absolute temperature, and $$M$$ is the molar mass.

Identify the proportionality.

Since $$R$$ and $$M$$ are constants for a given gas:

$$v_{\text{rms}} \propto \sqrt{T}$$

The RMS velocity is proportional to the square root of the absolute temperature.

The correct answer is Proportional to square root of temperature $$\sqrt{T}$$.