The moment of inertia of a semi circular disc of mass M and radius 'r' about a line perpendicular to the plane of disc through the centre is A) M(R×R) B) M(R×R)/2 C) M(R×R)/4 D) 2/5 M(R×R)
The moment of inertia is additive: if we have two objects having moments of inertia `I_1` and `I_2` with respect to the same axis, then the moment of inertia of the compound object (with respect to the same axis) will be `I_1+I_2.`
Therefore the moment of inertia of a semicircular disk (which I think is a half of a circular disk) is a half of the entire disk's moment of inertia.
Also, it is well known (or may be easily obtained by integration) that the moment of inertia of a circular disk or mass M and radius r (about a line perpendicular to the plane of disc through its center) is equal to
So for the semidisk the moment of inertia is `(M*r^2)/4,` option C.