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If C(1), C(2), C(3) ….. represent the sp...

If `C_(1), C_(2), C_(3) …..` represent the speeds on `n_(1), n_(2) , n_(3)…..` molecules, then the root mean square speed is

A

`((n_(1)C_(1)^(2)+n_(2)C_(2)^(2)+n_(3)C_(3)^(2)+"....")/(n_(1)+n_(2)+n_(3)+"...."))^(1//2)`

B

`((n_(1)C_(1)^(2)+n_(2)C_(2)^(2)+n_(3)C_(3)^(2)+".....")^(1//2))/(n_(1)+n_(2)+n_(3)+"....)`

C

`((n_(1)C_(1)^(2))^(1//2))/(n_(1))+((n_(2)C_(2)^(2))^(1//2))/(n_(2))+((n_(3)C_(3)^(2)))/(n_(3))+"....."`

D

`[((n_(1)C_(1)+n_(2)C_(2)+n_(3)C_(3)+"....")^(2))/((n_(1)+n_(2)+n_(3)+"....."))]^(1//2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`n_(1)` molecules have speeed equal to `C_(1)n_(2)` molecules have speed equal to `C_(2)` , and so on …..
Thus the addition of square of velocities
`= n_(1).C_(1)^(2) +n_(2).C_(2)^(2)+n_(3).C_(3)^(2)+`-------
Mean square speed
`=(n_(1)C_(1)^(2) +n_(2)C_(2)^(2)+n_(3)C_(3)^(2)+ " ------")/(n_(1)+n_(2)_n_(3)+"----")`
Root mean square speed
` = sqrt((n_(1)C_(1)^(2)+n_(2)C_(2)^(2)+n_(3)C_(3)^(2)+"----")/(n_(1)+n_(2)+n_(3)+"----"))`
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