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`N (lt 100)` molecules of a gas have velocities 1,2,3….N km/s respectively. ThenA. rms speed and average speed of molecules is sameB. ratio of rms speed to average speed is `sqrt((2N+1))(N+1)//6N`C. ratio of rms speed to average speed is `sqrt((2N + 1))(N+1)//6`D. ratio of rms speed to average speed of molecules is `sqrt(((2n+1))/(6(N+1)))` |
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Answer» Correct Answer - D `V_("rms")=sqrt((V_(1)^(2)+V_(2)^(2)+.......V_(N)^(2))/(N))=sqrt((1^(2)+2^(2)+.......+ N^(2))/(N))` `=sqrt((N(N+1)(2N+1))/(6N))rArr V_("rms")=sqrt(((N+1)(2N+1))/(6))` `V_("avg")=(V_(1)+V_(2)+......+V_(N))/(N)` `=(1+2+......+N)/(N)=(N(N+1))/(2N)=(N+1)/(2)` `(V_("rms"))/(V_("avg"))=2 sqrt(((2N+1))/(6(N+1)))`. |
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