We will have the following:
[tex]F=\frac{mv^2}{r}\Rightarrow26.6N=\frac{(0.250kg)(9.00m/s)^2}{r}[/tex][tex]\Rightarrow r=\frac{(0.250kg)(9.00m/s)^2}{26.6N}\Rightarrow r=\frac{405}{532}m[/tex][tex]\Rightarrow r\approx0.761m[/tex]So, the radius of the circle the yoyo is moving is approximately 0.761 meters.
