$(1)$ \[ R\cdot \sin\theta=F\] \[ \therefore F-R\cdot \sin\theta=0 \] $(2)$ \[R\cdot \cos\theta =mg\] \[ \therefore -mg+R\cdot \cos\theta=0 \] $(3)$ \[ F=m r \omega^2 = m r \left(\frac{v}{r} \right)^2=m\cdot \frac{v^2}{r}\] \[ \therefore F=m\cdot \frac{v^2}{r} \] $(4)$ \[ \frac{R\cdot \sin\theta}{R\cdot \cos\theta}=\tan\theta=\frac{m\cdot \frac{v^2}{r}}{mg}=\frac{v^2}{rg}\] \[ \therefore \theta=\tan^{-1}\left(\frac{v^2}{rg} \right) \] $(5)$ \[ \theta=\tan^{-1}\left\{\frac{\left(30\times 10^3 \times \frac{1}{3600}\,\rm{m/s} \right)^2}{40\,\rm{m}\times9.81\,\rm{m/s^2}} \right\} =10.03^\circ\] \[ \therefore \theta=10.0^\circ \]