Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. A thin plate of constant density that is symmetric about the x-axis has a center of mass with an x-coordinate of zero.b. A thin plate of constant density that is symmetric about both the x-axis and the y-axis has its center of mass at the origin.c. The center of mass of a thin plate must lie on the plate.d. The center of mass of a connected solid region (all in one piece) must lie within the region.

Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. A thin plate of constant density that is symmetric about the x-axis has a center of mass with an x-coordinate of zero.b. A thin plate of constant density that is symmetric about both the x-axis and the y-axis has its center of mass at the origin.c. The center of mass of a thin plate must lie on the plate.d. The center of mass of a connected solid region (all in one piece) must lie within the region.