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# The ratio between the root mean square speed of $H_2$ at 50K and that of $O_2$ at 800K is..

$(a)\;4\qquad(b)\;2\qquad(c)\;1\qquad(d)\;\large\frac{1}{4}$

$U_{rms}\;\;\;H_2 = \sqrt{[\large\frac{3\times50\times R}{2}]}$
$U_{rms}\;\;\;O_2 = \sqrt{[\large\frac{3\times800\times R}{32}]}$
$\therefore \large\frac{U_{rms}H_2}{U_{rms}O_2} = \large\frac{3\times50\times32}{2\times3\times800}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=1$