The `rms` velocity molecules of a gas of density `4 kg m^(-3)` and pressure `1.2 xx 10^(5) N m^(-2)` is

Options

A. 1
B. 1.22
C. 1.12
D. Data are not sufficient

Answer

To find the root mean square (RMS) velocity of the molecules of a gas given its density and pressure, we can use the formula:

\[ V_{rms} = \sqrt{\frac{3P}{D}} \]

where:
- \( V_{rms} \) is the root mean square velocity,
- \( P \) is the pressure of the gas,
- \( D \) is the density of the gas.

### Step-by-Step Solution:

1. **Identify the given values**:
- Density \( D = 4 \, \text{kg/m}^3 \)
- Pressure \( P = 1.2 \times 10^5 \, \text{N/m}^2 \)

2. **Substitute the values into the formula**:
\[ V_{rms} = \sqrt{\frac{3 \times (1.2 \times 10^5)}{4}} \]

3. **Calculate the numerator**:
- First, calculate \( 3 \times 1.2 \times 10^5 \):
\[ 3 \times 1.2 = 3.6 \]
\[ 3.6 \times 10^5 = 360000 \]

4. **Divide by the density**:
\[ \frac{360000}{4} = 90000 \]

5. **Take the square root**:
\[ V_{rms} = \sqrt{90000} \]
\[ V_{rms} = 300 \, \text{m/s} \]

### Final Answer:
The root mean square velocity of the gas molecules is \( 300 \, \text{m/s} \).