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. \[\text{ }\!\!\rho\!\!\text{ mixture=}\frac{\text{mass}\,\text{of}\,{{\text{O}}_{\text{2}}}\,\text{+mass}\,\text{of}\,{{\text{H}}_{\text{2}}}}{\text{volume}\,\text{of}\,{{\text{O}}_{\text{2}}}\text{+volume}\,\text{of}\,{{\text{H}}_{\text{2}}}}\] \[=\frac{32+2}{V+V}\] \[=\frac{34}{2V}=\frac{17}{V}\] also, \[\rho {{H}_{2}}=\frac{2}{V}\] Now, velocity \[\upsilon ={{\left( \frac{\gamma P}{\rho } \right)}^{\frac{1}{2}}}\]or\[\upsilon \propto \frac{1}{\sqrt{\rho }}\] \[\therefore \] \[\frac{\upsilon \text{mixture}}{^{\upsilon }{{H}_{2}}}=\sqrt{\left( \frac{^{\rho }{{H}_{2}}}{\rho \text{mixture}} \right)}\] \[=\sqrt{\left( \frac{2/V}{17/V} \right)}=\sqrt{\left( \frac{2}{17} \right)}\]
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