Five molecules of a gas have speeds 1, 2, 4, | vedclass

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Question

(B) The root mean square $(V_{RMS})$ velocity is defined as the square root of the mean of the squares of the individual speeds.Given speeds are $V_1

Vedclass · Accepted Answer

$8.2$

Vedclass · Answer

(B) The root mean square $(V_{RMS})$ velocity is defined as the square root of the mean of the squares of the individual speeds.Given speeds are $V_1 = 1 \, m/s$,$V_2 = 2 \, m/s$,$V_3 = 4 \, m/s$,$V_4 = 8 \, m/s$,and $V_5 = 16 \, m/s$.The formula for $V_{RMS}$ is:$V_{RMS} = \sqrt{\frac{V_1^2 + V_2^2 + V_3^2 + V_4^2 + V_5^2}{N}}$Substituting the values:$V_{RMS} = \sqrt{\frac{1^2 + 2^2 + 4^2 + 8^2 + 16^2}{5}}$$V_{RMS} = \sqrt{\frac{1 + 4 + 16 + 64 + 256}{5}}$$V_{RMS} = \sqrt{\frac{341}{5}}$$V_{RMS} = \sqrt{68.2} \approx 8.258 \, m/s$.Rounding to the nearest provided option,we get $8.2 \, m/s$.

Five molecules of a gas have speeds $1, 2, 4, 8$ and $16 \, m/s$ at some instant. The root mean square velocity of the gas molecules is ..... $m/s$.

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