Question

The velocity of three molecules is 3v, 4v and 5v find their r.m.s velocity​

Answer 1

Answer:

$\sqrt{9v { }^{2} + 16v { }^{2} + 25v {}^{2} \div 3 } = \sqrt{16.6v {}^{2} } = 4.1v$

Answer 2

The rms velocity of the three molecules is $\sqrt{\dfrac{50}{3}}v$

Explanation:

The velocity of three molecules is 3v, 4v and 5v. The root mean square velocity is given by :

$V=\sqrt{\dfrac{v_1^2+v_2^2+....+v_n^2}{n}}$

$V=\sqrt{\dfrac{(3v)^2+(4v)^2+(5v)^2}{3}} \\\\V=\sqrt{\dfrac{50v^2}{3}} \\\\V=\sqrt{\dfrac{50}{3}}v$

So, the rms velocity of the three molecules is $\sqrt{\dfrac{50}{3}}v$. Hence, this is the required solution.

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