Question

Four molecules of a gas have speeds $1,2,3$ and $4\, kms ^{-1}$. The value of rms speed of the gas molecules is :

• A. $\frac{1}{2} \sqrt{15} kms ^{-1}$
• B. $\frac{1}{2} \sqrt{10} kms ^{-1}$
• C. $2.5 \,kms^{-1}$
• D. $\frac{15}{2} kms ^{-1}$

Answer 1

Answer: (D)

The square root of $\bar{v}^{2}$ is called the root mean square velocity (rms) speed of the molecules.
$v_{ rms } =\sqrt{\bar{v}^{2}}$
$=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}}{4}}$
$=\sqrt{\frac{(1)^{2}+(2)^{2}+(3)^{2}+(4)^{2}}{4}}$
$=\sqrt{\frac{1+4+9+16}{4}}$
$=\sqrt{\frac{30}{4}}$
$=\sqrt{\frac{15}{2}} kms ^{-1}$