Three particles have speeds of 2u,10u,and 11u | vedclass

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Question

(A) The root mean square (r.m.s.) speed is given by $V_{rms} = \sqrt{\frac{(2u)^2 + (10u)^2 + (11u)^2}{3}} = \sqrt{\frac{4u^2 + 100u^2 + 121u^2}{3}} =

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The r.m.s. speed exceeds the mean speed by about $u$.

Vedclass · Answer

(A) The root mean square (r.m.s.) speed is given by $V_{rms} = \sqrt{\frac{(2u)^2 + (10u)^2 + (11u)^2}{3}} = \sqrt{\frac{4u^2 + 100u^2 + 121u^2}{3}} = \sqrt{\frac{225u^2}{3}} = \sqrt{75}u = 5\sqrt{3}u \approx 8.66u$.The mean (average) speed is given by $V_{avg} = \frac{2u + 10u + 11u}{3} = \frac{23u}{3} \approx 7.66u$.Comparing the two values,$V_{rms} - V_{avg} \approx 8.66u - 7.66u = 1u$.Therefore,the r.m.s. speed exceeds the mean speed by about $u$.

Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

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