Centres of gravity (C.G.) of common plane figures Identify the incorrect statement about the location of the centre of gravity (centroid) of the listed shapes.

Introduction / Context:Remembering centroid locations of standard shapes is crucial for area moments, composite sections, and structural design. One of the statements below is intentionally wrong to test precise recall.

Given Data / Assumptions:

• Plane laminae of uniform thickness and density.
• Standard geometric shapes: circle, triangle, rectangle, semicircle, ellipse.

Concept / Approach:

For symmetric figures, the centroid lies at the intersection of symmetry axes. For semicircular area, the centroid lies along the axis of symmetry at a known distance from the circle’s centre, but it is not r/2.

Step-by-Step Solution:

Verification / Alternative check:

Using tabulated centroid formulae, the semicircle’s area centroid from the base is 4r/(3π) relative to the circle centre along the symmetry line, confirming (d) is wrong.

Why Other Options Are Wrong:

Here only (d) is wrong; the others match standard results.

Common Pitfalls:

Confusing the centroid of a semicircular arc (2r/π) with that of a semicircular area (4r/(3π)); mixing distances from base versus from centre.

Final Answer:

The C.G. of a semicircle is at a distance of r/2 from the centre.