JEE Advanced 2016 · Paper 2, Physics question 16

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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 $\vec F_{rot}$ experienced by a particle of mass $m$ moving on the rotating disc and the force $\vec F_{in}$ experienced by the particle in an inertial frame of reference is
$$\vec F_{rot}=\vec F_{in}+2m(\vec v_{rot}\times\vec\omega)+m(\vec\omega\times\vec r)\times\vec\omega,$$
where $\vec v_{rot}$ 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 centre 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 axis $(\vec\omega=\omega\hat k)$. A small block of mass $m$ is gently placed in the slot at $\vec r=(R/2)\hat i$ at $t=0$ and is constrained to move only along the slot.