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Q.
The rms speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, - 2, - 4, - 6) \,m/s$ is :
Delhi UMET/DPMTDelhi UMET/DPMT 2004
Solution:
Square-root of the mean square velocity of gas molecules,
is called root-mean-square velocity (rms).
$v_{r m s}=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+\ldots v_{N}^{2}}{N}}$
Given $v_{1}=6\, m / s$,
$v_{2}=4\, m / s , $
$v_{3}=2 \,m / s , $
$v_{4}=0 \,m / s$,
$v_{5}=-2\, m / s ,$
$ v_{6}=-4 \,m / s , $
$v_{7}=-6 \,m / s .$
$\therefore U_{\text{rms}}=\sqrt{\frac{(6)^{2}+(4)^{2}+(2)^{2}}{(-2)^{2}+(-4)^{2}+(-6)^{2}}}$
$=\sqrt{\frac{112}{7}}=\sqrt{16}=4\, m / s$