A) \[\sqrt{8}\]
B) \[\sqrt{2/17}\]
C) \[\sqrt{1/8}\]
D) \[\sqrt{32/17}\]
Correct Answer: B
Solution :
Let one mole of each gas has same volume as\[V\]. When they are mixed, then density of mixture is \[{{\rho }_{\operatorname{mixture}}}=\frac{mass\,\,of\,\,{{O}_{2}}+mass\,\,of\,\,{{H}_{2}}}{volume\,\,of\,\,{{O}_{2}}+volume\,\,of\,\,{{H}_{2}}}\] \[=\frac{32+2}{V+V}=\frac{34}{2V}=\frac{17}{V}\] Also,\[{{\rho }_{{{H}_{2}}}}=\frac{2}{V}\] Now, velocity\[v={{\left( \frac{\gamma p}{\rho } \right)}^{1/2}}\]or\[v\propto \frac{1}{\sqrt{\rho }}\] \[\frac{{{v}_{mixture}}}{{{v}_{{{H}_{2}}}}}=\sqrt{\left( \frac{{{\rho }_{{{H}_{2}}}}}{{{\rho }_{mixture}}} \right)}\] \[=\sqrt{\left( \frac{2/V}{17/V} \right)}=\sqrt{\left( \frac{2}{17} \right)}\]
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