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. `300 ms^(-1)`
B. `900 ms^(-1)`
C. `120 ms^(-1)`
D. `600 ms^(-1)`

Explanation

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

### Step 1: Understand the Formula
The formula for the root mean square velocity (v_rms) of a gas is given by:
\[ v_{rms} = \sqrt{\frac{3P}{\rho}} \]
where:
- \( P \) is the pressure of the gas,
- \( \rho \) is the density of the gas.

### Step 2: Identify the Given Values
From the question, we have:
- Density (\( \rho \)) = 4 kg/m³
- Pressure (\( P \)) = \( 1.2 \times 10^5 \) N/m²

### Step 3: Substitute the Values into the Formula
Now, we can substitute the values of pressure and density into the formula:
\[ v_{rms} = \sqrt{\frac{3 \times (1.2 \times 10^5)}{4}} \]

### Step 4: Calculate the Value
First, calculate the numerator:
\[ 3 \times (1.2 \times 10^5) = 3.6 \times 10^5 \]

Now, substitute this back into the equation:
\[ v_{rms} = \sqrt{\frac{3.6 \times 10^5}{4}} \]

Next, calculate the division:
\[ \frac{3.6 \times 10^5}{4} = 0.9 \times 10^5 = 9.0 \times 10^4 \]

Now, take the square root:
\[ v_{rms} = \sqrt{9.0 \times 10^4} = 300 \, \text{m/s} \]

### Final Answer
The root mean square velocity of the molecules of the gas is:
\[ v_{rms} = 300 \, \text{m/s} \]

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