Chapter 13 - Kinetics of a Particle: Force and Acceleration - Section 13.5 - Equations of Motion: Normal and Tangential Coordinates - Problems - Page 146: 53

$r=1.36m$

We can determine the required radius as follows: $\Sigma F_y=ma_y$ $\implies T-147.15N=0$ $\implies T=147.15N$ and $\Sigma F_n=ma_n$ $\implies T=m\frac{v^2}{r}$ We plug in the known values to obtain: $147.15=2(\frac{(10)^2}{r})$ This simplifies to: $r=1.36m$