A) 516 metre/sec
B) 450 metre/sec
C) 410 metre/sec
D) 746 metre/sec
Correct Answer: A
Solution :
Since from the formula rms speed \[({{V}_{rms}})\] is directly proportional to square of temperature i.e., \[{{V}_{rms}}\propto \sqrt{T}\] For two cases, we have \[\frac{{{V}_{rms}}(1)}{{{V}_{rms}}(2)}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] Here, \[{{V}_{rms}}(1)=400m/\sec .\] \[{{T}_{1}}={{27}^{o}}C,\,{{T}_{2}}={{227}^{o}}C\] \[\frac{400}{{{V}_{rms\,(2)}}}=\sqrt{\frac{27+273}{227+273}}\] \[\frac{400}{{{V}_{rms\,(2)}}}=\sqrt{\frac{300}{500}}\] \[\Rightarrow \] \[{{V}_{rms\,(2)}}=\sqrt{\frac{500}{300}}\times 400\] \[\Rightarrow \] \[{{V}_{rms\,(2)}}=1.29\times 400=516.39\] \[{{V}_{rms\,(2)}}\approx 516m/s\]
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