Center of Gravity of a Uniform Lamina

Definition: The center of gravity of a uniform lamina is a point on the axis of symmetry of the lamina where the whole weight of the lamina can be considered to act. This point is also called the centroid or center of mass.

Midpoint of Its Axis

The correct answer is option 'C': the midpoint of its axis. The centroid of a uniform lamina lies on its axis of symmetry. The axis of symmetry is the line that divides the lamina into two equal parts, such that each part is a mirror image of the other.

The centroid of a uniform lamina is located at the midpoint of its axis. This is because the weight of the lamina is distributed uniformly throughout its area, and the center of gravity of each small element of the area lies on the axis of symmetry. Therefore, the centroid of the whole lamina must lie on the axis of symmetry, and at its midpoint.

Center of a Heavy Portion

Option 'A': the center of a heavy portion is incorrect. The center of a heavy portion is not necessarily the same as the center of gravity or centroid of the lamina. The center of a heavy portion is the point where the weight of the portion can be considered to act. This point depends on the distribution of mass within the portion, and may not coincide with the centroid of the whole lamina.

Bottom Surface

Option 'B': the bottom surface is also incorrect. The center of gravity or centroid of a lamina does not necessarily lie on its bottom surface. The location of the centroid depends on the shape and symmetry of the lamina, and may not coincide with any particular surface.

Conclusion

In conclusion, the correct answer is option 'C': the midpoint of its axis. The centroid of a uniform lamina lies on its axis of symmetry, and at its midpoint. This point is where the whole weight of the lamina can be considered to act.