# In a gas, 5 molecules have speed 150 m/s, 170 m/s, 170 m/s, 180 m/s, 190 m/s. Ratio of $V_r_m_s$ to $V_m_e_a_n$ is nearly Option 1) 1 Option 2) 3 Option 3) 0.5 Option 4) 1.53

As we learnt in

Root mean square velocity -

$V_{rms}= \sqrt{\frac{3RT}{M}}$

$= \sqrt{\frac{3P}{\rho }}$

- wherein

R = Universal gas constant

M = molar mass

P = pressure due to gas

$\rho$ = density

Average speed of molecule of a gas -

$V_{av}= \sqrt{\frac{8KT}{\pi m}}$

$= \sqrt{\frac{8RT}{\pi m}}$

- wherein

K = Boltzmann's Constant

m = mass of a molecule

R = Universal gas constant

T = temperature

$V_{rms}=\sqrt{\frac{V{_{1}}^{2}+V{_{2}}^{2}+V{_{3}}^{2}+V{_{4}}^{2}+V{_{5}}^{2}}{5}}= 172.51\ m/s$

$V_{mean}=\frac{150+170+170+ 180+190}{5}$$=\frac{860}{5}=172\ m/s$

Ratio = 1

Option 1)

1

correct

Option 2)

3

Incorrect

Option 3)

0.5

Incorrect

Option 4)

1.53

Incorrect

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