Answer
a) $a_c=3\times10^5m/s^2$
b) $a_c=3.06\times10^4g$
Work Step by Step
a) Turbine blades rotate at $617rev/s$, so the period of rotation is $T=1/617=1.62\times10^{-3}s$
We also have $r=0.02m$
We know that $$T=\frac{2\pi r}{v}=\frac{2\pi r}{\sqrt{a_cr}}=\frac{2\pi\sqrt r}{\sqrt{a_c}}$$ $$\sqrt{a_c}=\frac{2\pi\sqrt r}{T}$$ $$a_c=\frac{4\pi^2r}{T^2}$$
Plug $T$ and $r$: $$a_c=3\times10^5m/s^2$$
b) $a_c=\frac{3\times10^5m/s^2}{9.8m/s^2}g=3.06\times10^4g$