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BITSAT2019PhysicsRotational MotionActual

A semicircular disc of mass M and radius R is free to rotate about its diameter. The moment of inertia of semicircular disc about a line perpendicular to its plane through centre is

Options

  1. A3 4 M R 2
  2. BM R 2 2
  3. CM R 2 3
  4. DM R 2 4

Correct answer

B. M R 2 2

Step-by-step solution

The moment of inertia of disc of radius R about its axis is I = M ' R 2 2 where, M ' = mass of complete disc = 2 M I = 2 M R 2 2 I = M R 2       . . . i If I 1 be the moment of inertia of semicircular disc about its. axis, then disc may be assumed as combination of two semi-circular parts, Thus, I = I 1 + I 1 ⇒ I 1 = I 2 = M R 2 2

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