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A flat surface of a thin uniform disk A of radius R is glued to...

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed ω about the vertical axis passing through the center of A. The angular momentum of B is nMωR2 with respect to the center of A. Which of the following is the value of n?

​​​​​​​

2
5
72
92
Solution:

The centre of mass of B has angular velocity ω about the centre of A. Therefore, the velocity of the centre of B is

VB=ω2R.

The point of contact of A and B is at rest therefore, the angular velocity of B will be,

ωB=vBR=2ω

Now the angular momentum of B with respect to centre of A

L=MvBr+ICMωB

L=Mω2R2R+MR222ω

L=5MR2ω

Comparing the magnitude with nMωR2

n=5