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 w². Then w²/v²

        (a)    2

        (b)    1

        (c)    1/3

        (d)    2/3

Question

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 w². Then w²/v²

(a) 2

(b) 1

(c) 1/3

(d) 2/3

Amit Saxena · Answer

(d) Mean kinetic energy of the two types of molecules should be equal. The mean square velocity of A type molecules = w 2 + w 2 + w 2 = 3w 2 . Therefore, This gives m 2 /v 2 = 2/3

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