JEE Advanced 2016 Paper 2 Physics Q15

Physics · Rotation

Problem

PARAGRAPH 1 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 ω⃗\vec\omega is an example of a non-inertial frame of reference. The relationship between the force F⃗rot\vec F_{\rm rot} experienced by a particle of mass mm moving on the rotating disc and the force F⃗in\vec F_{\rm in} experienced by the particle in an inertial frame of reference is F⃗rot=F⃗in+2m(v⃗rot×ω⃗)+m(ω⃗×r⃗)×ω⃗,\vec F_{\rm rot}=\vec F_{\rm in}+2m(\vec v_{\rm rot}\times\vec\omega)+m(\vec\omega\times\vec r)\times\vec\omega, where v⃗rot\vec v_{\rm rot} is the velocity of the particle in the rotating frame of reference and r⃗\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 RR rotating counter-clockwise with a constant angular speed ω\omega about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the xx-axis along the slot, the yy-axis perpendicular to the slot and the zz-axis along the rotation axis (ω⃗=ωk^\vec\omega=\omega\hat k). A small block of mass mm is gently placed in the slot at r⃗=(R/2)i^\vec r=(R/2)\hat i at t=0t=0 and is constrained to move only along the slot. The distance rr of the block at time tt is

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