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AP EAMCET201921 Apr 2019Evening ShiftPhysicsMotion in Two DimensionsActual

A uniform rod of length l and density ρ is revolving about a vertical axis passing through its one end. If ω is the angular velocity of the rod then the centrifugal force per unit area of the rod is

Options

  1. Aρ ω 2 l 2 4
  2. Bρ ω 2 l 2 12
  3. Cρ ω 2 l 2 2
  4. Dρ ω 2 l 2 8

Correct answer

C. ρ ω 2 l 2 2

Step-by-step solution

Take an element of length d x and mass d m at a distance x from the rotating end. Here mass of elemental part d m = ρ d x Centrifugal force on this small element d F = d m   x ω 2 Total centrifugal force, F = ∫ d F = ∫ 0 l ρ x ω 2 d x ⇒     F = ρ ω 2 l 2 2

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