Question

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

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Answer 2

The ratio of their r.m.s.  velocity and the average velocity will be 1.1.

Explanation:

The root mean square velocity is given as

$v_{rms} =\sqrt{\frac{(v_1)^2+(v_2)^2+(v_3)^2+.....(v_n^2)}{n} }$

As given respective speeds of the molecules are 1,2,3,4,5 km/s, then

  $v_{rms} =\sqrt{\frac{(1)^2+(2)^2+(3)^2+(4)^2+(5)^2)}{5} }$

$v_{rms} =\sqrt{\frac{55}{5} } =\sqrt{11}$

$v_{rms}=3.32km/s$

The average speed of the molecules is given as

$v_a_g=\frac{v_1+v_2+v_3+v_4+....v_n}{n}$

Substitute the values, we get

$v_a_g=\frac{1+2+3+4+5}{5} =3 km/s$

Ratio,

$\frac{v_{rms} }{v_a_g}=\frac{3.32}{3}$

       =  1.1

Thus, the ratio of their r.m.s.  velocity and the average velocity will be 1.1.

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