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(A) Given,the speeds of the five molecules are $v_1=1, v_2=2, v_3=3, v_4=4, v_5=5 \ km/s$.The root mean square (rms) speed is given by:$v_{rms} = \sqr

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$\sqrt{11}: 3$

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(A) Given,the speeds of the five molecules are $v_1=1, v_2=2, v_3=3, v_4=4, v_5=5 \ km/s$.The root mean square (rms) speed is given by:$v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2 + v_5^2}{5}} = \sqrt{\frac{1^2 + 2^2 + 3^2 + 4^2 + 5^2}{5}} = \sqrt{\frac{1 + 4 + 9 + 16 + 25}{5}} = \sqrt{\frac{55}{5}} = \sqrt{11} \ km/s$.The average speed is given by:$v_{av} = \frac{v_1 + v_2 + v_3 + v_4 + v_5}{5} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3 \ km/s$.The ratio of rms velocity to average velocity is:$\frac{v_{rms}}{v_{av}} = \frac{\sqrt{11}}{3} = \sqrt{11}: 3$.

The respective speeds of the five molecules are $1, 2, 3, 4$ and $5 \ km/s$. The ratio of their root mean square (rms) velocity to their average velocity is:

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