GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

A uniform disc with radius r and a mass of 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 ω, when viewed from the right-hand side bearing, Q. The axle processes about a vertical axis at ${\mathit{\omega }}_{\mathit{p}}=\mathit{\omega }/10$ in the clockwise direction when viewed from above. Let ${\mathit{R}}_{\mathit{e}}$ and ${\mathit{R}}_{\mathit{Q}}$ (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings $\mathit{P}$ and $\mathit{Q}$, respectively. Assuming ${\mathit{\omega }}^2\mathit{r}=300\mathit{m}/{\mathit{s}}^2$ and $\mathit{g}=10\mathit{m}/{\mathit{s}}^2$, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is