MHT CET · Physics · Kinetic Theory of Gases
Six molecules of a gas in container have speeds \(2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}\), \(6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}\) and \(5 \mathrm{~m} / \mathrm{s}\). The r.m.s. speed is
- A \(4 \mathrm{~m} / \mathrm{s}\)
- B \(1.7 \mathrm{~m} / \mathrm{s}\)
- C \(4 \cdot 24 \mathrm{~m} / \mathrm{s}\)
- D \(5 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(C) \(4 \cdot 24 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\( v_{rms} = \sqrt{\frac{\sum v_i^2}{n}} \) \( v_{rms} = \sqrt{\frac{2^2 + 5^2 + 3^2 + 6^2 + 3^2 + 5^2}{6}} = \sqrt{\frac{4 + 25 + 9 + 36 + 9 + 25}{6}} = \sqrt{\frac{108}{6}} \)
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