Q. If a gas contains only three molecules that move with velocities of 100, 200, 500 ${ms}^{- 1}.$ What is the rms velocity of that gas in ${ms}^{- 1}?$
A) $100\frac{\sqrt{8}}{3}$
B) $100\ \sqrt{30}$
C) $100\ \sqrt{10}$
D) $\frac{800}{3}$
Explanation
(c)
$C_{1} = 100\ {ms}^{- 1},\ C_{2} = 200\ {ms}^{- 1},\ C_{3} = 500\ {ms}^{- 1}$
rms velocity $(C) = ?$
rms velocity $(C) = \sqrt{\frac{C_{1}^{2} + \ C_{2}^{2} + \ C_{3}^{2}}{n}}$
$= \sqrt{\frac{(100)^{2} + (200)^{2} + (500)^{2}}{3}}$
$= \sqrt{1,00,000} = 100\sqrt{10}\ {ms}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.