Question

# The speed of sound in a gas is $$V$$. If the rms velocity of gas molecules is C$$_{rms}$$ then the value of $$\displaystyle \frac{V}{\quad C_{rms}}$$ will be

A
3γ
B
γ3
C
3γ
D
γ3

Solution

## The correct option is B $$\displaystyle \sqrt{\frac{\gamma}{3}}$$Speed of sound $$V = \sqrt{\dfrac{\gamma RT}{M}}$$rms velocity of gas molecules $${C}_{rms} = \sqrt{3\dfrac{RT}{M}}$$$$\dfrac{V}{{C}_{rms}} = \sqrt{\dfrac{\gamma}{3}}$$Answer is D.Physics

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