Question

the velocities of the molecules are v, 2v, 3v, 4v and 5v. the RMS speed will b:

a. 11v
b. v (11)^12
c. v
d. v(12)^11


also xplain it

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Answer 1

How to Calculate RMS speed?

1. Do square of all observations/velocities
2. Take out their mean i.e., dividing by total number of observations
3. Now square the whole equation

Basically, you need to read Root Mean Square as inverse i.e., Square, then Mean and then Root.

It seems you mean to write v(11)^(1/2) so Option (b) is the appropriate answer.

Answer:

→ Option (B)

Answer 2

Answer:

Given :-

• Velocity 1 = v
• Velocity 2 = 2v
• Velocity 3 = 3v
• Velocity 4 = 4v
• Velocity 5 = 5v

To Find :-

RMS

Solution :-

RMS speed is calculated by

$\large \sf \: \sqrt{ \dfrac{v_1 {}^{2} + v_2 {}^{2} + v_3 {}^{2} + ... \: v_ 5 {}^{2} }{n} }$

$\large \sf \: RMS = \sqrt{ \dfrac{ {v}^{2} + {2v}^{2} + 3 {v}^{2} + 4 {v}^{2} + 5 {v}^{2} }{5} }$

$\large \sf \: RMS = \sqrt{ \dfrac{ {v}^{2} + 4 {v}^{2} + 9 {v}^{2} + 16 {v}^{2} + 25 {v}^{2} }{5} }$

$\large \sf \: RMS = \sqrt{ \dfrac{55 {v}^{2} }{5} }$

RMS = √v11

RMS = v11^½