Q. Four molecules of a gas have speeds 1, 2, 3 and 4 $kms^{- 1}$. The value of rms speed of the gas molecules is
A) $\frac{1}{2}\sqrt{15}\ kms^{- 1}$
B) $\frac{1}{2}\ \sqrt{10}\ kms^{- 1}$
C) $2.5\ kms^{- 1}$
D) $\sqrt{\frac{15}{2}}\ kms^{- 1}$
Explanation
(d) The square root of ${\overline{v}}^{2}$ is called the root mean square velocity (rms) speed of the molecules.
$v_{rms} = \sqrt{{\overline{v}}^{2}} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{3} + v_{4}^{4}}{4}}$
$= \ \sqrt{\frac{(1)^{2} + (2)^{2} + (3)^{2} + (4)^{2}}{4}}$
$\ = \ \ \ \sqrt{\frac{1 + 4 + 9 + 16}{4}} = \ \sqrt{\frac{30}{4}} = \sqrt{\frac{15}{2}}\ kms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.