The respective speeds of the five molecules are 1,2,3,4 and $5 \mathrm{kms}^{-1}$. Then, the ratio of their…
The respective speeds of the five molecules are 1,2,3,4 and $5 \mathrm{kms}^{-1}$. Then, the ratio of their rms velocity and the average velocity will be
$\sqrt{11}: 3$
$3: \sqrt{11}$
$1: 2$
$3: 4$
Solution
Given, speed of five molecules be $v_1, v_2, v_3, v_4$ and $v_5=1,2,3,4$ and $5 \mathrm{kms}^{-1}$
Since, root mean square speed,
$
v_{\mathrm{rms}}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+v_4^2+v_5^2}{5}}
$
and average speed,
$
v_{\mathrm{av}}=\frac{v_1+v_2+v_3+v_4+v_5}{5}
$
On dividing Eq. (i) by Eq. (ii), we get
$
\begin{aligned}
\frac{v_{\mathrm{rms}}}{v_{\mathrm{av}}} & =\frac{\sqrt{1^2+2^2+3^2+4^2+5^2}}{1+2+3+4+5} \times \frac{5}{\sqrt{5}} \\
& =\frac{\sqrt{11}}{3} \text { or } \sqrt{11}: 3
\end{aligned}
$