Answer
$A\lt C \lt B$
Work Step by Step
We know that
For A
$\frac{a_{c,new}}{a_{c,old}}=\frac{v_{new}^2/r_{new}^2}{v_{old}^2/r_{old}^2}=(\frac{v_{new}}{v_{old}})^2(\frac{r_{old}}{r_{new}})=(\frac{v_{old}}{v_{old}})^2(\frac{r_{old}}{\frac{1}{2}r_{old}})=2$
For B
$\frac{a_{c,new}}{a_{c,old}}=\frac{v_{new}^2/r_{new}^2}{v_{old}^2/r_{old}^2}=(\frac{v_{new}}{v_{old}})^2(\frac{r_{old}}{r_{new}})=(\frac{\frac{1}{3}v_{old}}{v_{old}})^2(\frac{r_{old}}{r_{old}})=\frac{1}{9}$
For C
$\frac{a_{c,new}}{a_{c,old}}=\frac{v_{new}^2/r_{new}^2}{v_{old}^2/r_{old}^2}=(\frac{v_{new}}{v_{old}})^2(\frac{r_{old}}{r_{new}})=(\frac{v_{old}}{v_{old}})^2(\frac{r_{old}}{4r_{old}})=\frac{1}{4}$
Now we can rank A, B and C in order of decreasing centripetal acceleration as
$A\lt C \lt B$
