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The speeds of $5$ molecules of a gas (in arbitary units) are as follows $2, 3, 4, 5, 6$ . The root mean square speed for these molecules is-

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$2.91$

$3.52$

$4.00$

$4.24$

answer is D.

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Detailed Solution

$v_{r . m . s .} = \sqrt{\frac{v_{1}^{2} + v_{2}^{2} + v_{3}^{2} + v_{4}^{2} + v_{5}^{2}}{5}} = \sqrt{\frac{2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2}}{5}} = 4.24 m / s$

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