Question

A gas consists of $5$ molecules with a velocity of $5{\text{m s}}^{-1}$, $10$ molecules with a velocity of $3{\text{m s}}^{-1}$ and $6$ molecules with a velocity of $6{\text{m s}}^{-1}$. The ratio of average velocity and rms velocity of the molecules is $9.5\times {10}^{-x}$. Value of $x$ is:

Answer 1

Average velocity is the average of the velocities of all the gases
$=\frac{5\times 5+10\times 3+6\times 6}{21}=4.33$
rms velocity is the square root of the mean of the squares of the velocities.
$=\sqrt{\frac{5\times 25+10\times 9+6\times 36}{21}}=4.53$
$\therefore \frac{V_{\text{av}}}{V_{\text{rms}}}=0.955=9.5\times {10}^{-1}$