Question

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

• A. $\sqrt{11}:3$
• B. $3:\sqrt{11}$
• C. 1 : 2
• D. 3 : 4

Answer 1

Answer: (A)

$\sqrt{11}:3$

Answer 2

$v_{rms} = \sqrt{\frac{1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2}}{5}} = \sqrt{11}km/s$

$v_{av} = \frac{1 + 2 + 3 + 4 + 5}{5} = 3km/s$Ž$\frac{v_{rms}}{v_{av}} = \frac{\sqrt{11}}{3}$