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

Question

The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/s. The ratio of their rms velocity and the average velocity will be (A)  √11:3  (B)  3:√11  (C) 1: 2 (D) 3: 4

Tardigrade Admin · Accepted Answer

vrms=√((1)2+(2)2+(3)2+(4)2+(5)2/5) =√11 km/s vav=(1+2+3+4+5/5)=3 km/s ∴ (vrms/vav)=(√11/3)

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

$11 : 3$

$3 : 11$

1 : 2

3 : 4

$v_{r m s} = \frac{( 1 ) ^{2} + ( 2 ) ^{2} + ( 3 ) ^{2} + ( 4 ) ^{2} + ( 5 ) ^{2}}{5}$ $= 11 km / s$ $v_{a v} = \frac{1 + 2 + 3 + 4 + 5}{5} = 3 km / s$ $∴$ $\frac{v _{r m s}}{v _{a v}} = \frac{11}{3}$

Q. The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/s. The ratio of their rms velocity and the average velocity will be

11​:3

3:11​