A) 1.5 m/s
B) 3.4 m/s
C) 9 m/s
D) 4 m/s
Correct Answer: D
Solution :
Square-root of the mean square velocity of gas molecules, is called root-mean-square velocity (rms). \[{{v}_{rms}}=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+...v_{N}^{2}}{N}}\] Given \[{{v}_{1}}=6\,m/s\], \[{{v}_{2}}=4\,m/s,\,\,{{v}_{3}}=2\,m/s,\,\,{{v}_{4}}=0\,m/s\], \[{{v}_{5}}=-2\,m/s,\,\,{{v}_{6}}=-4\,\,m/s,\,\,{{v}_{7}}=-6\,m/s\]. \[\therefore \] \[{{U}_{rms}}=\sqrt{\frac{\frac{{{(6)}^{2}}+{{(4)}^{2}}+{{(2)}^{2}}}{{{(-2)}^{2}}+{{(-4)}^{2}}+{{(-6)}^{2}}}}{7}}\] \[=\sqrt{\frac{112}{7}}=\sqrt{16}=4\,m/s\]
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