Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a…

Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, right rod of length l=24a through their center. 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 ω . The angular momentum of the entire assembly about the point 'O' is L→ (see the figure). Which of the following statement(s) is(are) true?

  1. The magnitude of angular momentum of the assembly about its center of mass is 17 ma2ω2
  2. The magnitude of the z - component of L→ is 55 ma2ω
  3. The magnitude of angular momentum of center of mass of the assembly about the point O is 81 ma2ω
  4. The center of mass of the assembly rotates about the z-axis with an angular speed of ω5

Solution

Magnitude of angular momentum of the assembly about its centre of mass =
ma22ω+4m 2a22ω=17ma22ω .

Asked in: JEE Advanced 2016 (Paper 2)

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