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AP EAMCET202120 Aug 2021Morning ShiftPhysicsRotational MotionActual

Four spheres each of diameter ' 2 a ' and mass ' m ' are placed in a way that their centers lie on the four cormers of a square of side b '. Moment of inertia of the system about an axis along one of the sides of the square is

Options

  1. A8 5 m a 2
  2. B4 5 m a 2 + 5 m b 2
  3. C4 5 m a 2 + 2 m b 2
  4. D8 5 m a 2 + 2 m b 2

Correct answer

D. 8 5 m a 2 + 2 m b 2

Step-by-step solution

Let A B is the axis about which we have to find the moment of inertia, the moment of inertia of the system is the summation of the moment of inertia of each sphere about A B   axis, I = I A + I B + I C + I D I A = I B = 2 5 m a 2 Using the parallel axis theorem for the sphere C   and   D ∴   I   of  C   about   A B = I   of  C  about   C D + m b 2 I C = I D = 2 5 m a 2 + m b 2 So, I = I A + I B + I C + I D I = 2 5 m a 2 + 2 5 m a 2 + 2 5 m a 2 + m b

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