The velocities of three molecules are 3u,4u and 5u, respectively. Then, rms speed will be

Options

A. `sqrt(50/3)v`
B. `sqrt(5/2)v`
C. `7/2V`
D. `5/2V`

Answer

To find the root mean square (RMS) speed of the three molecules with velocities 3u, 4u, and 5u, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the velocities of the molecules**:
- Let the velocities be:
- \( V_1 = 3u \)
- \( V_2 = 4u \)
- \( V_3 = 5u \)

2. **Square the velocities**:
- Calculate the squares of each velocity:
- \( V_1^2 = (3u)^2 = 9u^2 \)
- \( V_2^2 = (4u)^2 = 16u^2 \)
- \( V_3^2 = (5u)^2 = 25u^2 \)

3. **Sum the squares of the velocities**:
- Add the squared values:
\[ V_1^2 + V_2^2 + V_3^2 = 9u^2 + 16u^2 + 25u^2 = 50u^2 \]

4. **Divide by the number of molecules**:
- Since there are 3 molecules, we divide the sum by 3:
\[ \frac{V_1^2 + V_2^2 + V_3^2}{3} = \frac{50u^2}{3} \]

5. **Take the square root**:
- Finally, take the square root to find the RMS speed:
\[ V_{rms} = \sqrt{\frac{50u^2}{3}} = \frac{\sqrt{50}u}{\sqrt{3}} = \frac{5\sqrt{2}u}{\sqrt{3}} \]

### Final Answer:
The RMS speed of the three molecules is:
\[ V_{rms} = \frac{5\sqrt{2}u}{\sqrt{3}} \]