The y-components of velocities of the molecules of a gas are
-7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7 `ms^(-1)` then the rms velocity is

Options

A. `sqrt(56/3)ms^(-1)`
B. `sqrt(28/3)ms^(-1)`
C. `sqrt(112/3)ms^(-1)`
D. `sqrt(84/3)ms^(-1)`

Answer

A

Explanation

Given, Y-components of velocities are,
-7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7 `ms^(-1)`
As rms velocity,
`v_(rms)=sqrt((v_(1)^(2)+v_(2)^(2)+...+v_(n)^(2))/2)`
`" "=sqrt(((-7)^(2)+(-6)^(2)+...+0+_...+6^(2)+7^(2))/15)`
Since, `(-x)^(2)=x^(2)`
`rArr v_(rms)=sqrt((2(7^(2)+6^(2)+5^(2)+4^(2)+3^(2)+2^(2)+1^(2)))/(15))`
`v_(rms)=sqrt((2 times 140)/15)=sqrt(56/3)`
Hence, the rms speed is `sqrt(56/3)m//s`.