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JEE Main20206 Sep 2020Morning ShiftPhysicsRotational MotionActual

Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is M , radius of its top is R and height, H , then its moment of inertia about its axis is

Options

  1. AMR 2 2
  2. BM R 2 + H 2 4
  3. CMH 2 3
  4. DMR 2 3

Correct answer

A. MR 2 2

Step-by-step solution

It can be assumed as several parts of discs having different radius, so I = ∫ dl = ∫ dm r 2 From diagram r y = tan θ = R H r = R H · y dm = ρ π r 2 dy From equation (i), (ii) and (iii) I = M R 2 2

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