Answer
$2.12$
Work Step by Step
Recall: $v_{rms}=\sqrt {\frac{3k_{B}T}{m}}$
$\implies \frac{v_{rms,2}}{v_{rms,1}}=\frac{\sqrt {\frac{3k_{B}T_{2}}{m}}}{\sqrt {\frac{3k_{B}T_{1}}{m}}}=\frac{\sqrt {T_{2}}}{\sqrt {T_{1}}}=\frac{\sqrt {(1000+273)K}}{\sqrt {(10+273)K}}$
$=2.12$
