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MHT CET202523 Apr 2025Evening ShiftPhysicsKinetic Theory of GasesActual

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

Options

  1. A4 ~m / s
  2. B1.7 ~m / s
  3. C4 24 ~m / s
  4. D5 ~m / s

Correct answer

C. 4 24 ~m / s

Step-by-step solution

The root-mean-square speed is calculated using v_ rms = v₁^2 + v₂^2 + + v_n^2 n . Given speeds of 2 m/s, 5 m/s, 3 m/s, 6 m/s, 3 m/s, and 5 m/s, the squares are 4 , 25 , 9 , 36 , 9 , and 25 m²/s². The sum is v_i^2 = 4 + 25 + 9 + 36 + 9 + 25 = 108 m²/s², leading to a mean of 108 6 = 18 m²/s². Thus, v_ rms = 18 4.2426 m/s. This corresponds to the option C .

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