JEE Advanced 2016 Paper 2

Next 2 questions are based on the paragraph A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of a non-inertial frame of reference. The relationship between the force $\vec{F}_{\text{rot}}$ experienced by a particle of mass m moving on the rotating disc and the force $\vec{F}_{\text{in}}$ experienced by the particle in an inertial frame of reference is$\vec{F}_{\text{rot}} = \vec{F}_{\text{in}} \left( \vec{\upsilon}_{\text{rot}} \times \vec{\omega} \right) + m \left( \vec{\omega} \times \vec{r} \right) \times \vec{\omega}$where$\vec{\upsilon}_{\text{rot}}$ is the velocity of the particle in the rotating frame of reference and $\vec{r}$ is the position vector of the particle with respect to the center of the disc.Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $\omega$about its vertical axis through its center.We assign a coordinate system with the origin at the center of the disc, the x-axis along the slot the y-axis perpendicular to the slot and the z-axis along the rotation $(\omega = \omega \hat{k})$.A small block of mass m is gently placed in the slot at $\vec{r} = \frac{R}{\hat{2i}}$ at $t=0$ and is constrained to move only along the slot