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MHT CET202617 April 2026Morning ShiftPhysicsKinetic Theory of GasesActual

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

Options

  1. A2 5 : 1
  2. B5 : 1
  3. C1 : 2 5
  4. D5 : 2

Correct answer

D. 5 : 2

Step-by-step solution

The average velocity is given by: v_ avg = 1 + 2 + 3 + 4 + 5 + 6 + 7 7 = 28 7 = 4 km/s The root mean square (r.m.s.) velocity is given by: v_ rms = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 7 v_ rms = 140 7 = 20 = 2 5 km/s The ratio of r.m.s. velocity to average velocity is: v_ rms v_ avg = 2 5 4 = 5 2 Answer: 5 : 2

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