A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of $3 \mathrm{rad} /$ s . If the block slides along the slot with a constant speed of $0.2 \mathrm{~m} / \mathrm{s}$ relative to the slot, then the magnitude of Coriolis acceleration in $\mathrm{m} / \mathrm{s}^2$ is

A rigid circular disc of radius $r$ (in m ) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad s-1). The velocities (in $\mathrm{m} \mathrm{s}^{-1}$ ) at points O and A , respectively, are

The figure shows a schematic of a simple Watt governor mechanism with the spindle O₁O₂ rotating at an angular velocity ω about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O₁ is denoted by h. The value of h = 400 mm at a certain ω. If ω is doubled, the value of h will be _________ mm.

In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counter-clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is _____________