The r.m.s. speed of a group of 7 gas molecule | vedclass

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(D) The root mean square (r.m.s.) speed is defined as the square root of the mean of the squares of the individual speeds.Formula: $v_{rms} = \sqrt{\f

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The root mean square (r.m.s.) speed is defined as the square root of the mean of the squares of the individual speeds.Formula: $v_{rms} = \sqrt{\frac{\sum v_i^2}{N}}$Given speeds are $6, 4, 2, 0, -2, -4, -6 \, m/s$ and $N = 7$.Calculating the sum of squares: $v_{rms} = \sqrt{\frac{6^2 + 4^2 + 2^2 + 0^2 + (-2)^2 + (-4)^2 + (-6)^2}{7}}$$v_{rms} = \sqrt{\frac{36 + 16 + 4 + 0 + 4 + 16 + 36}{7}}$$v_{rms} = \sqrt{\frac{112}{7}}$$v_{rms} = \sqrt{16} = 4 \, m/s$.

The r.m.s. speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, -2, -4, -6) \, m/s$ is ...... $m/s$.

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