An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $\mu$, as shown in the figure. At some time, an impulse $J_0 \hat{x}$ is applied at a height $h$ above the center of the disk. If $h=h_m$ then the disk rolls without slipping along the $x$-axis.
Which of the following statement(s) is(are) correct?
Select ALL correct options:
A
For $\mu \neq 0$ and $a \rightarrow 0, h_m=b / 2$.
B
For $\mu \neq 0$ and $a \rightarrow b, h_m=b$.
C
For $h=h_m$, the initial angular velocity does not depend on the inner radius $a$.
D
For $\mu=0$ and $h=0$, the wheel always slides without rolling.
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