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Q.

Speed of sound wave in a gas is υ₁ and r.m.s speed of molecules of the gas at the same temperature is υ₂. Then

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a

υ₁ = υ₂

b

υ₁ > υ₂

c

υ₁ $\leq$ υ₂

d

υ₁ < υ₂

answer is B.

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Detailed Solution

Speed of sound in the gas, $v_{1} = \sqrt{\frac{γ R T}{M}}$

RMS speed of gas molecule, $v_{2} = \sqrt{\frac{3 R T}{M}}$

For any gas, $γ < 3$

$∴ v_{1} < v_{2}$

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