A uniform disc with radius $r$ and a mass $m$ kg is mounted centrally on a horizontal axle of negligible mass and length of $1.5r$. The disc spins counter-clockwise about the axle with angular speed $\omega$, when viewed from the right-hand side bearing, Q. The axle processes about a vertical axis at $\omega_p=\omega/10$ in the clockwise direction when viewed from above. Let $R_P$ and $R_Q$ (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming $\omega^2r=300 m/s^2$ and $g=10 m/s^2$, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is ______
