Four molecules have speeds `2 m//s, 3 km//s, 4 km//s` and `5 km//s`. The `rms` speed of these molecules in `km//s` is

Options

A. `sqrt(27)/(2)`
B. `sqrt(27)`
C. `2sqrt(27)`
D. `sqrt(54)`

Answer

A

Explanation

`bar(v^(2)) = (v_(1)^(2) + v_(2)^(2) + v_(3)^(2) + v_(4)^(2))/(N)`
`= ((2)^(2) + (3)^(2) + (4)^(2) + (5)^(2))/(4)`
`= 27//2`
`v_(rms) = sqrt(bar(v^(2))) = sqrt((27)/(2))km//s`