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Two thin circular discs of mass m and 4m...

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(24a)` through their centres. 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 `omega.` The angular momemtum of the entire assembly about the point 'O' is `vacL` (see the figure). Which of the follwing statement (s) is (are) true?

A

The magnitude of angular momentum of the assembly about its center of mass is `17ma^(2)omega//2`

B

The magnitude of the z-component of `vec(L)` is `55 ma^(2) omega`

C

The magnitude of angular momentum of centre of mass of the assembly about the point O is `81 "ms"^(2) omega`

D

The centre of mass of the assembly rotates about the z- axis with an angular speed of `omega//5`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`costheta=(1)/(sqrt(l^(2)+a^(2)))=(sqrt(24)a)/(sqrt(25)a)=(sqrt(24))/(5)`
`omega_(z)=(omegaa)/(l)costheta=(omegaxxa)/(sqrt(24)a)xx(sqrt(24))/(5)=(omega)/(5)`
`L_(CM)=(ma^(2))/(2)omega+(4m(2a)^(2))/(2)omega=(17ma^(2)omega)/(2)`
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