Final answer:
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 1/4MR².
Step-by-step explanation:
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 can be found using the formula for the moment of inertia of a disk.
The moment of inertia of a disk is given by the equation I = 1/2MR², where M is the mass of the disk and R is the radius of the disk.
Since a semicircular disc is half of a complete disk, the moment of inertia of a semicircular disc is half of the moment of inertia of a complete disk, which gives us a moment of inertia of 1/4MR² for the semicircular disc.
Therefore, the correct answer is A. 1/4Mr².