Centre of Mass & Rotational Motion · JEE Advanced previous year questions

2023 2 questions

1. Q212023 · 4 Jun 2023 · Paper 1

   A bar of mass $M=1.00\mathrm{kg}$ and length $L=0.20\mathrm{m}$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m=0.10\mathrm{kg}$ is moving on the same horizontal surface with $5.00\mathrm{m}{\mathrm{s}}^{-1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L/2$ from the pivoted end and returns back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity $\omega$. Which of the following statement is correct?

   1. A.$\omega =6.98\mathrm{rad}{\mathrm{s}}^{-1}$ and $\mathrm{v}=4.30\mathrm{m}{\mathrm{s}}^{-1}$
   2. B.$\omega =3.75\mathrm{rad}{\mathrm{s}}^{-1}$ and $\mathrm{v}=4.30\mathrm{m}{\mathrm{s}}^{-1}$
   3. C.$\omega =3.75\mathrm{rad}{\mathrm{s}}^{-1}$ and $\mathrm{v}=10.0\mathrm{m}{\mathrm{s}}^{-1}$
   4. D.$\omega =6.80\mathrm{rad}{\mathrm{s}}^{-1}$ and $\mathrm{v}=4.10\mathrm{m}{\mathrm{s}}^{-1}$
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   Answer: A

2. Q232023 · 4 Jun 2023 · Paper 2· One or more correct
   
   1. A.For $\mu \ne 0$ and $a\to 0$, $h_m=b/2$.
   2. B.For $\mu \ne 0$ and $a\to b$, $h_m=b$.
   3. C.For $h=h_m$, the initial angular velocity does not depend on the inner radius $a$.
   4. D.For $\mu =0$ and $h=0$, the wheel always slides without rolling.
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   Answer: A, B, C, D