Answer
$$
r=13.3 \mathrm{~mm}
$$
Work Step by Step
When $\theta=4 \mathrm{rad}, r=10 \mathrm{~mm}$
$$
\begin{aligned}
& T_s=0.015(4)=0.06 \mathrm{~N} \cdot \mathrm{m} \\
& F=\frac{0.06}{0.012}=5 \mathrm{~N} \\
& T_f=5(0.010)=0.05 \mathrm{~N} \cdot \mathrm{m} \text { (constant) }
\end{aligned}
$$
When $\theta=3 \mathrm{rad}$,
$$
\begin{aligned}
& T_s=0.015(3)=0.045 \mathrm{~N} \cdot \mathrm{m} \\
& F=\frac{0.045}{0.012}=3.75 \mathrm{~N}
\end{aligned}
$$
For the fusee require
$$
0.05=3.75 r
$$
$$
r=0.0133 \mathrm{~m}=13.3 \mathrm{~mm}
$$
