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Four molecules of a gas have speeds 1, 2, 3 and 4 km/s. The value of the r.m.s. speed of the gas molecules is

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$\frac{1}{2} \sqrt{15} km / s$

$\frac{1}{2} \sqrt{10} km / s$

$2.5 km / s$

$\sqrt{\frac{15}{2}} km / s$

answer is D.

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Detailed Solution

R.M.S. speed $= \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2} \dots v_{n}^{2}}{n}}; \bar{v} = \sqrt{\frac{1^{2} + 2^{2} + 3^{2} + 4^{2}}{4}}; \bar{v} = \sqrt{\frac{30}{4}}; \bar{v} = \sqrt{\frac{15}{2}}$

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