MCQ
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 $\mathrm{h}$ 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?
(image)
($A$) 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.
- A$A,D$
- B$A,B$
- C$A,B,C$
- ✓$A,B,C,D$
