The mean square velocity of the five molecules of velocities are 2 m/s, 3 m/s, 4 m/s, 5 m/s and 6 m/s respectively is

Options

A. 4.242(m//s)^(2)`
B. `(4m//s)^(2)`
C. `18(m//s)^(2)`
D. `16(m//s)^(2)`

Explanation

To find the mean square velocity of the five molecules with given velocities, we will follow these steps:

### Step-by-Step Solution:

1. **List the Velocities**:
The velocities of the five molecules are:
- \( V_1 = 2 \, \text{m/s} \)
- \( V_2 = 3 \, \text{m/s} \)
- \( V_3 = 4 \, \text{m/s} \)
- \( V_4 = 5 \, \text{m/s} \)
- \( V_5 = 6 \, \text{m/s} \)

2. **Calculate the Square of Each Velocity**:
- \( V_1^2 = (2 \, \text{m/s})^2 = 4 \, \text{m}^2/\text{s}^2 \)
- \( V_2^2 = (3 \, \text{m/s})^2 = 9 \, \text{m}^2/\text{s}^2 \)
- \( V_3^2 = (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 \)
- \( V_4^2 = (5 \, \text{m/s})^2 = 25 \, \text{m}^2/\text{s}^2 \)
- \( V_5^2 = (6 \, \text{m/s})^2 = 36 \, \text{m}^2/\text{s}^2 \)

3. **Sum the Squares**:
Now we will add all the squared velocities together:
\[ V_1^2 + V_2^2 + V_3^2 + V_4^2 + V_5^2 = 4 + 9 + 16 + 25 + 36 \]
\[ = 90 \, \text{m}^2/\text{s}^2 \]

4. **Calculate the Mean Square Velocity**:
The mean square velocity is calculated by dividing the total sum of squares by the number of molecules (which is 5):
\[ \text{Mean Square Velocity} = \frac{V_1^2 + V_2^2 + V_3^2 + V_4^2 + V_5^2}{5} = \frac{90 \, \text{m}^2/\text{s}^2}{5} \]
\[ = 18 \, \text{m}^2/\text{s}^2 \]

### Final Answer:
The mean square velocity of the five molecules is \( 18 \, \text{m}^2/\text{s}^2 \).

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