Final answer:
The center of mass of the lamina is at (0,2) due to the symmetry and variable mass density, which places more mass per unit area closer to the center, meaning option A is correct.
Step-by-step explanation:
The question asks to find the center of mass of a lamina in the shape of a circular ring with variable mass density σ(x, y) = σ₀/√(x² + y²), bounded between two circles x² + y² = 4 and x² + y² = 64, and located above the x-axis. To solve for the center of mass, we note that due to the symmetry of the lamina, the x-coordinate of the center of mass will be zero. To determine the y-coordinate of the center of mass, we would integrate the moment density over the area of the lamina and divide by the total mass. However, since the density function decreases with √(x² + y²) and due to the symmetry above the x-axis, we can infer without calculation that the center of mass must be closer to the smaller circle (radius 2) than to the larger one (radius 8), as the lamina has more mass per unit area closer to the center.
Thus, the correct answer is (0,2), or option A. We do not need to perform the full integration because the symmetry and density distribution provide enough information to determine the answer.