A) \[\sqrt{\frac{5}{42}}\]
B) \[\sqrt{\frac{5}{21}}\]
C) \[\frac{\sqrt{42}}{5}\]
D) \[\frac{\sqrt{21}}{5}\]
Correct Answer: C
Solution :
Velocity of sound in a gas \[v=\sqrt{\frac{\gamma \,p}{d}}\] \[\therefore \] \[\frac{{{v}_{{{H}_{2}}}}}{{{v}_{He}}}=\sqrt{\frac{{{\gamma }_{{{H}_{2}}}}\times {{d}_{He}}}{{{d}_{He}}\times {{\gamma }_{He}}}}\] \[\frac{{{H}_{2}}}{He}=\sqrt{\frac{7\times 3\times 2}{5\times 5}}\] As \[\frac{{{d}_{He}}}{{{d}_{{{H}_{2}}}}}=2\] \[\therefore \] \[\frac{{{v}_{{{H}_{2}}}}}{{{v}_{He}}}=\frac{\sqrt{42}}{5}\]
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