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N molecules each of mass m of a gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of B type is v² and the mean square rectangular component of the velocity of A type is denoted by ω². Then ω²/v²

1. 2
2. 1
3. 1/3
4. 2/3

Correct answer: 1/3

Solution

The mean square velocity of a gas molecule is proportional to the temperature and inversely proportional to its mass. For gas A, the mean square velocity is proportional to 1/m, and for gas B, it is proportional to 1/(2m). The mean square rectangular component of velocity is one-third of the mean square velocity. Thus, ω²/v² = (1/m) / (1/(2m)) × (1/3) = 1/3.

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