Which of the following expression does not give root mean square velocity ?

Options

A. `((3RT)/(M))^(1/2)`
B. `((3P)/(DM))^(1//2)`
C. `((3P)/(D))^(1//2)`
D. `((3PV)/(M))^(1//2)`

Explanation

To determine which expression does not give the root mean square (RMS) velocity, we first need to understand the standard formula for RMS velocity and then evaluate the options provided.

### Step-by-Step Solution:

1. **Understand the Root Mean Square Velocity Formula**:
The root mean square velocity (v_rms) of a gas is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas.

2. **Identify Alternative Forms**:
We can express the RMS velocity in different forms using the ideal gas law \( PV = nRT \) or \( PV = \frac{m}{M}RT \).
- For one mole of gas, we can express it as:
\[ v_{rms} = \sqrt{\frac{3PV}{M}} \]
- We can also express it in terms of density \( \rho \) (where \( \rho = \frac{m}{V} \)):
\[ v_{rms} = \sqrt{\frac{3P}{\rho}} \]

3. **Evaluate the Given Options**:
We need to check each option to see if it matches any of the valid expressions for RMS velocity.

4. **Identify the Incorrect Expression**:
- If an option does not match the standard forms or derivations of the RMS velocity, it is the one we are looking for.
- Based on the analysis, the only expression that does not represent the root mean square velocity is option **V**.

### Conclusion:
The expression that does not give the root mean square velocity is **option V**.