Solving one of the toughest Indian exam questions

This is Question 7 from the 2016 JEE Advanced Paper 2 physics section. Read the exam here: https://drive.google.com/file/d/0BxIR7Kj71SMKT2YtaFBPajRaOE0/view?usp=drive_open

The question covers rotational motion, angular velocity and angular momentum. Well done to any students who have completed JEE and good luck to those studying. In hindsight the final algebra isn't actually too bad, just annoying at the end of a long question.

The question was requested by comments on my previous video looking through JEE advanced 2016 paper 1: https://youtu.be/IpeL1prh2SY

I make videos about physics, math, astronomy and scientific beauty with a new episode every wednesday and sunday.

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The question:
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, rigid rod of length l = sqrt(24)a through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is w. The angular momentum of the entire assembly about the point ‘O’ is L.

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