A) \[{{U}_{rms}}=\sqrt{\frac{3E}{2M}}\]
B) \[{{U}_{rms}}=\sqrt{\frac{2E}{3M}}\]
C) \[{{U}_{rms}}=\sqrt{\frac{2E}{M}}\]
D) \[{{U}_{rms}}=\sqrt{\frac{E}{3M}}\]
Correct Answer: C
Solution :
Average kinetic energy, \[E=\frac{3}{2}RT\] .....(i) Root mean square velocity, \[{{U}_{rms}}=\sqrt{\frac{3RT}{M}}\] From eq. (i), \[RT=\frac{2E}{3}\] On putting the value of RT in the expression of \[{{U}_{rms}},\]we get \[{{U}_{rms}}=\sqrt{\frac{3\times 2E}{3M}}=\sqrt{\frac{2E}{M}}\]
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