JEE Advanced 2016 Paper 2

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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 ω is an example of a non-inertial frame of reference. The relationship between the force
F
rot
experienced by a particle of mass m moving on the rotating disc and the force
F
in
experienced by the particle in an inertial frame of reference is
F
rot
=
F
in
(
υ
rot
×
ω
)
+m(
ω
×
r
)
×
ω
where
υ
rot
is the velocity of the particle in the rotating frame of reference and
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 ωabout 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 (ω=ω
k
)
.A small block of mass m is gently placed in the slot at
r
=
R
2
i
at t=0 and is constrained to move only along the slot
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