A frame of the 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 `F_(ixt)` 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_(ixt) = F_(m) + 2m(V_(rxt) xx vecomega) + m(vec(omega) xx r) xx vec(omega)`, where, `v_(rxt)` 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 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 about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the z-axis along the rotation axis `(omega = omega k)`. A small block of mass m is gently placed in the slot at `r=(R//2)hatii` at t=0 and is constrained to move only along the slot

The distance r of the block at time t is

Options

A. `(R)/(4)(e^(2omegat)+e^(-2omegat))`
B. `(R)/(2)cos 2 omegat`
C. `(R)/(2)cos omegat`
D. `(R)/(2)(e^(omegat)+e^(-omegat))`

Answer

D