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JEE Main 2022 (29 Jun, Shift 1) · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from JEE Main 2022 (29 Jun, Shift 1)

Q42JEE Main 2022 · 29 JUN · SHIFT 1Medium

Angular Momentum & its Conservation

A spherical shell of 1 kg mass and radius R is rolling with angular speed ω\omega on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is a3\frac{a}{3} R2ω\omega. The value of a will be:

Figure

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Answer: (c)

  1. LO=Icmω+MvcmRL_O=I_{cm}\omega+Mv_{cm}R (O lies on the ground line, CM at height RR; both terms clockwise).
  2. Rolling: vcm=Rωv_{cm}=R\omega; shell: Icm=23MR2I_{cm}=\frac23MR^2, M=1M=1 kg.
  3. LO=23R2ω+R2ω=53R2ωL_O=\frac23R^2\omega+R^2\omega=\frac53R^2\omega
  4. So a=5a=5, answer (c).
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