Q. The velocity of 4 gas molecules are given by 1 km/s, 3 km/s, 5 km/s and 7 km/s. Calculate the difference between average and rms velocity.

A) 0.338
B) 0.438
C) 0.583
D) 0.683
Explanation

(c) The average velocity
$v_{av} = \frac{v_{1} + v_{2} + v_{3} + ... + v_{n}}{N}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1 + 3 + 5 + 7}{4}$ = 4 km/s
Root mean square velocity
$v_{rms} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2} + ... + v_{n}^{2}}{N}}$
$= \ \ \sqrt{\frac{1 + (3)^{2} + (5)^{2} + (7)^{2}}{4}}$
$= \ \ \sqrt{21} = 4.583$ km/s
Difference between average velocity and root mean square velocity
=4.583-4
=0.583 km/s

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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