A) 516 metre/sec
B) 450 metre/sec
C) 310 metre/sec
D) 746 metre/sec
Correct Answer: A
Solution :
We know that rms speed is directly proportional to square root of temperature \[{{\upsilon }_{rms}}\propto \sqrt{T}\] Hence, \[\frac{{{\upsilon }_{rms}}(1)}{{{\upsilon }_{rms}}(2)}\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[\frac{400}{{{\upsilon }_{rms}}(2)}=\frac{\sqrt{27+273}}{\sqrt{227+273}}\] \[=\sqrt{\frac{300}{500}}\] \[{{\upsilon }_{rms}}(2)=\upsilon \sqrt{\frac{500}{300}\times }400\] \[=1.29\times 400\] \[=516.39\text{ }m/s\] \[\approx 516\text{ }m/s\]
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