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

A. `(mr^2)/2`
B. `(mr^2)/4`
C. `(mr^2)/2+mx^2`
D. `(mr^2)/2-mx^2`

Explanation

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,
`I_c=I_(cm)+mx^2`
`I_(cm)=I_(c)-mx^2`
Here, `I_c=(mr)^2/2`
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)=(mr^2)/2-mx^2`