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MHT CET 2026 (17 Apr, Shift 1) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from MHT CET 2026 (17 Apr, Shift 1)

Q6MHT CET 2026 · 17 APR · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

The speeds of the seven molecules are 1, 3, 5, 7, 2, 4 and 6 km/s respectively. The ratio of their r.m.s. velocity and average velocity will be

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Answer: (d)

  1. Average speed vˉ=1+2+3+4+5+6+77=4 km/s\bar v = \frac{1+2+3+4+5+6+7}{7} = 4\text{ km/s}
  2. Mean square speed =1+4+9+16+25+36+497=1407=20= \frac{1+4+9+16+25+36+49}{7} = \frac{140}{7} = 20
  3. vrms=20=25 km/sv_{rms} = \sqrt{20} = 2\sqrt5\text{ km/s}
  4. vrmsvˉ=254=52\frac{v_{rms}}{\bar v} = \frac{2\sqrt5}{4} = \frac{\sqrt5}{2}
  5. So the answer is (d) 5:2\sqrt5 : 2.
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