If mean square of x- component of the velocity of molecules is denoted by -2- then R-M-S velocity of molecules will beA- -2-3B- 3 -2C- -D- -3

The correct option is B 3ω^2Let r.m.s velocity of nbsp; molecules be v_rms Given: Mean square of x component of the velocity of molecule, (v_x^2)=ω^2 Assumi ...

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Standard XII

Physics

Root Mean Square Speed

If mean squar...

Question

If mean square of $x -$ component of the velocity of molecules is denoted by $ω^{2}$ , then R.M.S velocity of molecules will be

ω

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\frac{ω^{2}}{3}

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3 ω^{2}

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\frac{ω}{3}

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Solution

The correct option is C $3 ω^{2}$
Let r.m.s velocity of molecules be $v_{rms}$
Given:
Mean square of $x -$ component of the velocity of molecule, $(v_{x}^{2}) = ω^{2}$
Assuming the gas to be isotropic,
$v_{x}^{2} = \frac{v_{rms}^{2}}{3}$
$∴ v_{rms}^{2} = 3 v_{x}^{2} = 3 ω^{2}$

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Root Mean Square Speed

Standard XII Physics

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If mean square of x− component of the velocity of molecules is denoted by ω2, then R.M.S velocity of molecules will be

The correct option is C 3ω2Let r.m.s velocity of molecules be vrms Given: Mean square of x− component of the velocity of molecule, (v2x)=ω2 Assuming the gas to be isotropic, v2x=v2rms3 ∴v2rms=3v2x=3ω2

If mean square of $x -$ component of the velocity of molecules is denoted by $ω^{2}$ , then R.M.S velocity of molecules will be

The correct option is C $3 ω^{2}$
Let r.m.s velocity of molecules be $v_{rms}$
Given:
Mean square of $x -$ component of the velocity of molecule, $(v_{x}^{2}) = ω^{2}$
Assuming the gas to be isotropic,
$v_{x}^{2} = \frac{v_{rms}^{2}}{3}$
$∴ v_{rms}^{2} = 3 v_{x}^{2} = 3 ω^{2}$