Q. The molecular velocities of two gases at the same temperature are $u_{1}$ and $u_{2}$ and their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions are correct?
A) $\frac{m_{1}}{u_{1}^{2}} = \frac{m_{2}}{u_{2}^{2}}$
B) $m_{1}u_{1} = m_{2}u_{2}$
C) $\frac{m_{1}}{u_{1}} = \frac{m_{2}}{u_{2}}$
D) $m_{1}u_{1}^{2} = m_{2}u_{2}^{2}$
Explanation
(d)
$\frac{u_{1}}{u_{2}} = \sqrt{\frac{m_{2}}{m_{1}} \times \frac{T_{1}}{T_{2}}}$
$\because\ T_{1} = T_{2}$
$So,\ \frac{u_{1}^{2}}{u_{2}^{2}} = \frac{m_{2}}{m_{1}}\ or\ u_{1}^{2}m_{1} = u_{2}^{2}m_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.