Answer
Please see the work below.
Work Step by Step
We know that
$\frac{u_{N_2}}{u_{O_2}}=(\frac{M_n(O_2)}{M_m(N_2)})^{\frac{1}{2}}$
We plug in the known values to obtain:
$\frac{u_{N_2}}{u_{O_2}}=(\frac{32.00}{28.02})^\frac{1}{2}=1.0686$
Hence the ratio of the rates of effusion of $N_2$ and $O_2$ is 1.0686 to 1.