A) 4v
B) 2v
C) \[\frac{v}{2}\]
D) \[\frac{v}{4}\]
Correct Answer: B
Solution :
The root mean square velocity is given by \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] So, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] Now, \[{{T}_{1}}=120K,\,{{T}_{2}}=480K,\,{{v}_{1}}=v\] So, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{120}{480}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{v}{{{v}_{2}}}=\frac{1}{2}\Rightarrow {{v}_{2}}=2v\]
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