Four particles have speed `2, 3, 4` and 5 cm/s respectively Their `RMS` speed is .

Options

A. 3.5 cm/s
B. (27/2) cm/s
C. `sqrt(54)` cm/s
D. `sqrt(54) //2` cm/s

Explanation

To find the root mean square (RMS) speed of the four particles with speeds 2 cm/s, 3 cm/s, 4 cm/s, and 5 cm/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the speeds of the particles**:
The speeds given are:
- \( v_1 = 2 \) cm/s
- \( v_2 = 3 \) cm/s
- \( v_3 = 4 \) cm/s
- \( v_4 = 5 \) cm/s

2. **Square each speed**:
We need to calculate the square of each speed:
- \( v_1^2 = 2^2 = 4 \)
- \( v_2^2 = 3^2 = 9 \)
- \( v_3^2 = 4^2 = 16 \)
- \( v_4^2 = 5^2 = 25 \)

3. **Sum the squared speeds**:
Now, we add these squared values together:
\[ v_1^2 + v_2^2 + v_3^2 + v_4^2 = 4 + 9 + 16 + 25 = 54 \]

4. **Divide by the number of particles**:
Since there are 4 particles, we divide the sum of the squares by 4:
\[ \text{Mean of squares} = \frac{54}{4} = 13.5 \]

5. **Take the square root**:
Finally, we take the square root of the mean of the squares to find the RMS speed:
\[ v_{\text{RMS}} = \sqrt{13.5} \]

6. **Calculate the final RMS speed**:
The square root of 13.5 can be approximated:
\[ v_{\text{RMS}} \approx 3.674 \text{ cm/s} \]

### Final Answer:
The RMS speed of the four particles is approximately \( 3.674 \) cm/s.

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