Let they be at closest distance after a time $t_1$

$w_1t_1+w_2t_2=\large\frac{2}{T}$

$t_1= \large\frac{2 \pi}{w_1+w_2}$

$\qquad= \large\frac{2 \pi}{(1.09+1.08) \times 10^{-3}}s$

$\qquad= \large\frac{2 \pi}{2.17 \times 10^{-3} \times 3600}$$hours$

$\qquad=0.8$ hours

Hence b is the correct answer