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AP EAMCET201920 Apr 2019Morning ShiftPhysicsRotational MotionActual

A semicircular plate of mass (m ) has radius (r ) and centre (c ). The centre of mass of the plate is at a distance (x ) from its centre (c ). Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

Options

  1. A( m r^2 2 )
  2. B( m r^2 4 )
  3. C( m r^2 2 +m x^2 )
  4. D( m r^2 2 -m x^2 )

Correct answer

D. ( m r^2 2 -m x^2 )

Step-by-step solution

Given, mass of a semicircular plate (=m ) radius of semicircular plate (=r ) According to the question we can drawn the following diagram, Now, from the parallel axis theorem, ( aligned I_c & =I_ cm +m x^2 I_ cm & =I_c-m x^2 Here, I_c & = m r^2 2 aligned ) Hence, moment of inertia of semicircular plate about an axis passing through its centre of mass and perpendicular to it's plane is (I_ cm = m r^2 2 -m x^2 )

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