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?

A

For $$\mu \neq 0$$ and $$a \to 0$$, $$h_m = b/2$$

B

For $$\mu \neq 0$$ and $$a \to b$$, $$h_m = b$$

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.