If three molecules of oxygen at 27°C have velocities 0.5 km/s, 1 km/s and 2 km/s respectively. Then their root mean square speed will be
A) 1.7 km/s
B) 1.32 km/s
C) 1.13 km/s
D) 1.17 km/s
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If three molecules of oxygen at 27°C have velocities 0.5 km/s, 1 km/s and 2 km/s respectively. Then their root mean square speed will be
A) 1.7 km/s
B) 1.32 km/s
C) 1.13 km/s
D) 1.17 km/s
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Explanation:
(Vrms)^2=V1^2+V2^2+V3^2 / 3
(Vrms)^2=0.25+1+4/3
(Vrms)^2=1.75
Vrms=1.323 km/s
Given:
Three molecules of oxygen at 27°C have velocities 0.5 km/s, 1 km/s and 2 km/s respectively.
To find:
RMS speed ?
Calculation:
[tex] \rm \: v_{RMS} = \sqrt{ \dfrac{ {(v_{1})}^{2} + {(v_{2})}^{2} + {(v_{3})}^{2}}{3} } [/tex]
[tex] \rm \implies\: v_{RMS} = \sqrt{ \dfrac{{(0.5)}^{2} + {(1)}^{2} + {(2)}^{2}}{3} } [/tex]
[tex] \rm \implies\: v_{RMS} = \sqrt{ \dfrac{0.25 + 1 + 4}{3} } [/tex]
[tex] \rm \implies\: v_{RMS} = \sqrt{ \dfrac{5.25}{3} } [/tex]
[tex] \rm \implies\: v_{RMS} = \sqrt{ 1.75 } [/tex]
[tex] \rm \implies\: v_{RMS} = 1.32 \: km/s[/tex]
So RMS velocity is 1.32 km/s.