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If a gas contains only three molecules that move with velocities of $100,200,500 \mathrm{~ms}^{-1}$. What is the rms velocity of that gas in $\mathrm{ms}^{-1}$ ?
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The correct answer is:
$100 \sqrt{10}$
$C_1=100 \mathrm{~ms}^{-1}, \quad C_2=200 \mathrm{~ms}^{-1}, \quad C_3=500 \mathrm{~ms}^{-1} \mathrm{rms}$ velocity $(C)=$ ?
$\operatorname{rms}$ velocity $(C)=\sqrt{\frac{C_1^2+C_2^2+C_3^2}{n}}$
$=\sqrt{\frac{(100)^2+(200)^2+(500)^2}{3}}$
$=\sqrt{100000}=100 \sqrt{10} \mathrm{~ms}^{-1}$
$\operatorname{rms}$ velocity $(C)=\sqrt{\frac{C_1^2+C_2^2+C_3^2}{n}}$
$=\sqrt{\frac{(100)^2+(200)^2+(500)^2}{3}}$
$=\sqrt{100000}=100 \sqrt{10} \mathrm{~ms}^{-1}$
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