The root mean square speed of one mole of a monoatomic gas having molecular mass M is $U_{rms}$. The relation between the average kinetic energy (E) of the gas and $U_{rms}$ is:

Question

$(a)\;U_{rms}=\sqrt{\large\frac{3E}{2M}}\qquad(b)\;U_{rms}=\sqrt{\large\frac{2E}{3M}}\qquad(c)\;U_{rms}=\sqrt{\large\frac{2E}{M}}\qquad(d)\;U_{rms}=\sqrt{\large\frac{E}{3M}}$$