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  4. The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/s. The ratio of their rms velocity and the average velocity will be

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Q. The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/s. The ratio of their $ rms $ velocity and the average velocity will be

VMMC MedicalVMMC Medical 2010

Solution:

$ {{v}_{rms}}=\sqrt{\frac{{{(1)}^{2}}+{{(2)}^{2}}+{{(3)}^{2}}+{{(4)}^{2}}+{{(5)}^{2}}}{5}} $ $ =\sqrt{11}\,\,km/s $ $ {{v}_{av}}=\frac{1+2+3+4+5}{5}=3\,km/s $ $ \therefore $ $ \frac{{{v}_{rms}}}{{{v}_{av}}}=\frac{\sqrt{11}}{3} $