Question

Five gas molecules chosen at random are found to have speed of $500\text{m/s},600\text{m/s},700\text{m/s},800\text{m/s}$ and $900\text{m/s}$. The approximate rms speed is :

• A. $600\text{m/s}$
• B. $900\text{m/s}$
• C. $500\text{m/s}$
• D. $714\text{m/s}$

Answer 1

The correct option is D $714\text{m/s}$

Given,
Speed of five random chosen molecules,
$v_1=500\text{m/s}$
$v_2=600\text{m/s}$
$v_3=700\text{m/s}$
$v_4=800\text{m/s}$
$v_5=900\text{m/s}$
We know that,
$v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+...+v_n^2}{n}}$
On putting all data,
$v_{rms}=\sqrt{\frac{{500}^2+{600}^2+{700}^2+{800}^2+{900}^2}{5}}$
$\Rightarrow v_{rms}\approx 714\text{m/s}$
The rms speed of five random chosen gas molecules is $714\text{m/s}$.