Root Mean Square Velocity calculation – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Root Mean Square Velocity calculation

Four particles have velocities 1, 0, 2 and 3 m/s. The root mean square velocity of the particles is
\(\sqrt{3.5} \text{m/s}\)
\(\sqrt{5.3} \text{m/s}\)
\(\sqrt{2.8} \text{m/s}\)
\(\sqrt{4.7} \text{m/s}\)

Solution:

The RMS velocity is given by \[v_{\text{rms}} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2}{4}}\]. Substituting the values, \[v_{text{rms}} = \sqrt{\frac{1^2 + 0^2 + 2^2 + 3^2}{4}} = \sqrt{\frac{14}{4}} = \sqrt{3.5} \text{m/s}\].

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