Question:
Six molecules of a gas in container have speeds 2 m/s, 5 m/s, 3 m/s, 6 m/s, 3 m/s, and 5 m/s. The r.m.s. speed is
Six molecules of a gas in container have speeds 2 m/s, 5 m/s, 3 m/s, 6 m/s, 3 m/s, and 5 m/s. The r.m.s. speed is
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RMS speed is always slightly higher than the average speed of the molecules.
Updated On: Apr 30, 2026
- 4 m/s
- 1.7 m/s
- 4.24 m/s
- 5 m/s
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The Correct Option is C
Solution and Explanation
Step 1: Formula
$v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + ... + v_n^2}{n}}$
Step 2: Sum of Squares
$\Sigma v^2 = 2^2 + 5^2 + 3^2 + 6^2 + 3^2 + 5^2$
$\Sigma v^2 = 4 + 25 + 9 + 36 + 9 + 25 = 108$
Step 3: Mean Square Speed
$v_{mean_square} = \frac{108}{6} = 18$
Step 4: Root Mean Square
$v_{rms} = \sqrt{18} \approx 4.24 \text{ m/s}$
Final Answer:(C)
$v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + ... + v_n^2}{n}}$
Step 2: Sum of Squares
$\Sigma v^2 = 2^2 + 5^2 + 3^2 + 6^2 + 3^2 + 5^2$
$\Sigma v^2 = 4 + 25 + 9 + 36 + 9 + 25 = 108$
Step 3: Mean Square Speed
$v_{mean_square} = \frac{108}{6} = 18$
Step 4: Root Mean Square
$v_{rms} = \sqrt{18} \approx 4.24 \text{ m/s}$
Final Answer:(C)
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