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

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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 &omega;  about the vertical axis passing through the center of A . The angular momentum of B is n M &omega; R 2  with respect to the center of A . Which of the following is the value of n ? ​​​​​​​

Quantrex Academy · Accepted Answer

Correct answer: B. 5

The centre of mass of  B  has angular velocity  &#969;  about the centre of  A . Therefore, the velocity of the centre of  B  is V B = &#969; 2 R . The point of contact of  A  and  B  is at rest therefore, the angular velocity of  B  will be, &#969; B = v B R = 2 &#969; Now the angular momentum of B  with respect to centre of  A L = M v B r + I C M &#969; B &#8658; L = M &#969; 2 R 2 R + M R 2 2 2 &#969; L = 5 M R 2 &#969; Comparing the magnitude with  n M &#969; R 2 n = 5

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