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Question

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?


A
2
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B
92
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C
5
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D
72
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Solution

The correct option is C 5
Angular momentum of B wrt center of A is
L=LCM+LBody about CM
L=(MR22)2ω ^k+Mω(2R)(2R) ^k
L=MR2ω ^k+4MR2ω ^k=5MR2ω ^k
Comparing the magnitude with nMR2ω, n=5
Hence, option (B) is correct.

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