Question

The moment of inertia of a uniform semicircular disc of mass `M` and radius `r` about a line perpendicular to the plane of the disc through the center is
A. `Mr^(2)`
B. `(1)/(2) MR^(2)`
C. `(1)/(4) Mr^(2)`
D. `(2)/(5) Mr^(2)`

Answer 1

Correct Answer - B
The mass of complete (circular) disc is
`M + M = 2M`
The moment of inertia of disc is
`I = (2Mr^(2))/(2)`

=`Mr^(2)`
Let the moment of inertia of semicircular disc is `I_(1)`. The disc may be assumed as combination of two semicircular parts.
Thus, `I_(1) = I - I_(2)`
`I_(1) = (I)/(2) = (Mr^(2))/(2)`.