Final answer:
The density of the rectangular plate varies along the sides. Option A is correct.
Step-by-step explanation:
The density of the plate varies along the sides of the plate. This means that the density is not constant throughout the entire plate. It can be higher or lower depending on the location within the plate.
For example, if we consider the corner points of the rectangular plate (0,0), (4,0), (4,4), and (0,4), the density would be minimum at the corners of the plate due to the lower mass and maximum at the center of the plate due to the higher mass.
So, the correct answer is (a) It varies along the sides of the plate.
The question refers to finding the center of mass and understanding the density distribution in various shapes like a rectangle, a rod, and modifications of cubes. It falls under the subject of physics, specifically mechanics, where mass distribution and its effects on the balance and motion of objects are studied.
We are introduced to the concept that density can vary in different ways; it can change linearly along the length of an object, quadratically, or be influenced by the position in a coordinate plane. These nuances are crucial in calculating the center of mass, which is the weighted average of the mass distribution of an object.