Answer
$$\frac{a_{c, sec}}{a_{c, min}}=3600$$
Work Step by Step
Since the hands are of the same length, $r_{sec}=r_{min}=r$
The second hand finishes 1 revolution in $60s$, so its speed $v_{sec}=\frac{1}{60}rev/s$
The minute hand finishes 1 revolution in $60min=3600s$, so its speed $v_{min}=\frac{1}{3600}rev/s$
Now we can compare $a_{c, sec}/a_{c, min}$
We know that $$a=\frac{v^2}{r}$$ Therefore, $$\frac{a_{c, sec}}{a_{c, min}}=\frac{\frac{v^2_{sec}}{r}}{\frac{v^2_{min}}{r}}=\Big(\frac{v_{sec}}{v_{min}}\Big)^2$$ $$\frac{a_{c, sec}}{a_{c, min}}=\Big(\frac{1/60}{1/3600}\Big)^2=60^2=3600$$
