Q7 / 160 · AP EAMCET 2003 · Chemistry

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 $\mathrm{ms}^{-1}$ ?

  • A
    $100 \frac{\sqrt{8}}{3}$
  • B
    $100 \sqrt{30}$
  • Correct answer
    C
    $100 \sqrt{10}$
  • D
    $\frac{800}{3}$

Solution

$C_1=100 \mathrm{~ms}^{-1}, \quad C_2=200 \mathrm{~ms}^{-1}, \quad C_3=500 \mathrm{~ms}^{-1} \mathrm{rms}$ velocity $(C)=$ ? $\operatorname{rms}$ velocity $(C)=\sqrt{\frac{C_1^2+C_2^2+C_3^2}{n}}$ $=\sqrt{\frac{(100)^2+(200)^2+(500)^2}{3}}$ $=\sqrt{100000}=100 \sqrt{10} \mathrm{~ms}^{-1}$

Hence, the correct answer is option: 'C'.

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