Question

# The root mean square speed of gas molecules is C$$_{rms}$$. The root mean square speed in a specific direction will be :

A
Crms
B
Crms3
C
Crms3
D
3Crms

Solution

## The correct option is C $$\dfrac{C_{rms}}{\sqrt{3}}$$$$C_{rms} = \sqrt{\bar{C^2}}$$$$\bar{C^2} = \bar{u^2} + \bar{v^2} + \bar{w^2}$$$$u^2=v^2=w^2$$$$\therefore \bar{C^2} = 3\bar{u^2}$$$$\Rightarrow \bar{u^2} =\dfrac{1}{3}\bar{C^2}$$$$\therefore u_{rms} = \sqrt{\bar{u^2}}=\sqrt{\dfrac{1}{3}\bar{C^2}}=\dfrac{1}{\sqrt{3}}C_{rms}$$Physics

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