# The average speed of molecules in a gas is given by:

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Answer is option (A)

From kinetic theory equation we have

Pressure (P) = 1/3 [m/V]Nc2 and so PV = 1/3 [mNc2]

Now the total mass of the gas M = mN, and since r = M/V we can write
Pressure (P) = 1/3 [ρc2]

average speed v = √(3p/ρ)