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Question
The velocity of the three molecules is 2 km s-1, 4 km s-1, 6 km s-1. Find (i) mean square velocity (ii) root mean square velocity.
Solution
Given:
v1 = 2 km/s, v2 = 4 km/s, v3 = 6 km/s,
To find:
- Mean square velocity
- Root mean square velocity
Formulae:
- `overline("v"^2) = ("v"_1^2 + "v"_2^2 + "v"_3^2)/3`
- vrms = `sqrt(("v"_1^2 + "v"_2^2 + "v"_3^2)/3)`
Calculation:
From formula (i),
`overline("v"^2) = (2^2 + 4^2 + 6^2)/3` = 18.66 km2/s2
From formula (ii),
vrms = `sqrt((2^2 + 4^2 + 6^2)/3) = sqrt18.66` = 4.319 km/s
- Mean square velocity is 18.66 km2/s2.
- Root mean square velocity 4.319 km/s.
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