Q. 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 precesses about a vertical axis at 𝜔𝑝 = 𝜔 ⁄ 10 in the clockwise direction when viewed from above. Let 𝑅𝑃 and 𝑅𝑄 (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming 𝜔2 𝑟 = 300 m/s2 and 𝑔 = 10 m/s2, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is
Ans: -3
Sol:
