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Four molecules of ags have speeds 1,2,3 ...

Four molecules of ags have speeds 1,2,3 and 4 `km//s`.The volue of the root mean square speed of the gas molecules is

A

`(1)/(2)sqrt(15)km//s`

B

`(1)/(2)sqrt(10)km//s`

C

`2.56 km//s`

D

`sqrt(15/2)km//s`

Text Solution

Verified by Experts

The correct Answer is:
D
`becauseV_(rms)=`sqrt(((V_(1)^(2)+V_(2)^(2)+…+V_(n)^(2))/(n))`
`V_(rms)= sqrt((1^(2)+2^(2)+3^(2)+4^(2)/(4))=sqrt(((1+4+9+16)/(4))`
`=sqrt((30)/(4))=sqrt((15)/(2))km//s`
`therefore` " "`V_(rms)=sqrt((15)/(2))km//s`
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