Physics · Rotational Dynamics
JEE Advanced 2023 — Paper 2 — Question 19
An annular disk of mass M , inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction , as shown in the figure. At some time, an impulse is applied at a height above the center of the disk. If then the disk rolls without slipping along the -axis. Which of the following statement(s) is(are) correct?
- Option A:Correct
For and
- Option B:Correct
For and
- Option C:Correct
For , the initial angular velocity does not depend on the inner radius a.
- Option D:Correct
For and , the wheel always slides without rolling.
Answer: A, B, C, D
Step-by-step solution
\mathrm{J}=\mathrm{Mv}_{\mathrm{cm}} …(i)
\end{gathered}$$
$$\begin{gathered}
\mathrm{Jh}=\mathrm{I}_{\mathrm{cm}} \omega …(ii)
\end{gathered}$$
$$\begin{gathered}
\mathrm{v}_{\mathrm{cm}}=\mathrm{b} \omega …(iii)
\end{gathered}$$
$\mathrm{h}=\frac{\mathrm{I}_{\mathrm{cm}}}{\mathrm{Mb}}$
(A) For $\mu \neq 0, \mathrm{a}=0$ the system will be a disc, for pure rolling of disc
\mathrm{h}=\frac{\mathrm{I}_{\mathrm{cm}}}{\mathrm{Mb}}=\frac{\mathrm{b}}{2}
(B) for $\mu \neq 0, \mathrm{a}=\mathrm{b}$ wheel will be ring $h=b$ (C) for $\mu=0$ and $h=0$ wheel will slide without rolling (D) for $\mathrm{h}=\mathrm{h}_{\mathrm{m}}, \mathrm{v}_{\mathrm{cm}}=\mathrm{v} \omega$Answer key and solution verified before publishing.
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- Exam
- JEE Advanced 2023
- Paper
- Paper 2
- Subject
- Physics
- Chapter
- Rotational Dynamics
- Topic
- Rolling Motion