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 centre of mass of B has fixed angular speed $ω$ about the vertical axis passing through the centre of A. The angular momentum of B is $n M ω R^{2}$ with respect to the centre of A. Which of the following is not the value of n?

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$7 / 2$

$9 / 2$

answer is A, C, D.

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Detailed Solution

$V_{C M} = 2 R ω$
At point of contact
$V_{C M} = ω_{0} R \Rightarrow ω_{0} = 2 ω$
Angular momentum of disk B with respect to centre of A is
Question Image
$L = (\frac{M R^{2}}{2}) (ω_{0}) + M (2 R ω) (2 R) = (\frac{M R^{2}}{2}) (2 ω) + 4 M R^{2} ω L = 5 M R^{2} ω ∴ n = 5.$