If \[{{C}_{1}},\,{{C}_{2}},\,{{C}_{3}}......\]represent the speeds of \[{{n}_{1}},\,{{n}_{2}},\,{{n}_{3}}.....\] molecules, then the root mean square speed is [IIT 1993]

\[\frac{{{({{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....)}^{1/2}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....}\]

\[{{\left( \frac{{{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....} \right)}^{1/2}}\]

\[\frac{{{({{n}_{1}}C_{1}^{2})}^{1/2}}}{{{n}_{1}}}+\frac{{{({{n}_{2}}C_{2}^{2})}^{1/2}}}{{{n}_{2}}}+\frac{{{({{n}_{3}}C_{3}^{2})}^{1/2}}}{{{n}_{3}}}+......\]

\[{{\left[ \frac{{{({{n}_{1}}{{C}_{1}}+{{n}_{2}}{{C}_{2}}+{{n}_{3}}{{C}_{3}}+....)}^{2}}}{({{n}_{1}}+{{n}_{2}}+{{n}_{3}}+....)} \right]}^{1/2}}\]

If \[{{C}_{1}},\,{{C}_{2}},\,{{C}_{3}}......\]represent the speeds of

1.	If \[{{C}_{1}},\,{{C}_{2}},\,{{C}_{3}}......\]represent the speeds of \[{{n}_{1}},\,{{n}_{2}},\,{{n}_{3}}.....\] molecules, then the root mean square speed is [IIT 1993]
A.	\[{{\left( \frac{{{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....} \right)}^{1/2}}\]
B.	\[\frac{{{({{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....)}^{1/2}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....}\]
C.	\[\frac{{{({{n}_{1}}C_{1}^{2})}^{1/2}}}{{{n}_{1}}}+\frac{{{({{n}_{2}}C_{2}^{2})}^{1/2}}}{{{n}_{2}}}+\frac{{{({{n}_{3}}C_{3}^{2})}^{1/2}}}{{{n}_{3}}}+......\]
D.	\[{{\left[ \frac{{{({{n}_{1}}{{C}_{1}}+{{n}_{2}}{{C}_{2}}+{{n}_{3}}{{C}_{3}}+....)}^{2}}}{({{n}_{1}}+{{n}_{2}}+{{n}_{3}}+....)} \right]}^{1/2}}\]
Answer» B. \[\frac{{{({{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....)}^{1/2}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....}\]

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