Final answer:
The moment of inertia of a uniform square plate about an axis passing through one corner and perpendicular to the plane of the plate is (1/24)(m)(a^4).
Step-by-step explanation:
The moment of inertia of a uniform square plate about an axis passing through one corner and perpendicular to the plane of the plate can be determined by considering it as a combination of two rectangles. Let's divide the square plate into two identical rectangles, with one rectangle having length "a" and width "a/2". The moment of inertia of a rectangle about an axis through one corner and perpendicular to the plane can be calculated as (1/12)mL^2, where m is the mass and L is the length of the rectangle.
So, the moment of inertia of one rectangle is (1/12)(m)(a)(a/2)^2. Since there are two identical rectangles, the total moment of inertia of the square plate is 2[(1/12)(m)(a)(a/2)^2]. By simplifying this equation, we get (1/6)(m)(a^2)(a^2/4) = (1/24)(m)(a^4).Using parallel axis theorem, along with the known moment of inertia for a square plate about an axis through its center, can help solve this problem. However, given the provided references are about rods and discs, the specific answer for a square plate isn't directly given, but the concepts from rods and disks might be combined and adapted to solve for a square plate by considering the plate as a collection of rods.