Centres of Gravity — Solid Hemisphere A solid hemisphere of radius r has its centre of gravity located at a distance 3r/8 from the flat base along the symmetry axis. Is this statement correct?

Introduction / Context: Locating the centre of gravity (centroid for uniform density) of standard 3D solids is a common requirement in statics and strength of materials. For a solid hemisphere, there is a well-established distance of the centroid from the flat face (base).

Given Data / Assumptions:

• Solid hemisphere of radius r, uniform density.
• Distance measured from the plane face (base) along the central vertical axis.

Concept / Approach: The centroid of a solid hemisphere lies closer to the base than to the sphere centre. Standard integration (using disks or spherical coordinates) yields a compact result: ȳ = 3r/8 from the base plane toward the curved surface along the symmetry axis.

Step-by-Step Solution:

Verification / Alternative check: Tabulated centroid locations in handbooks (solids of revolution) list ȳ = 3r/8 for the solid hemisphere, while the spherical surface (hemispherical shell) has a different value: ȳ = r/2 from the base.

Why Other Options Are Wrong: 'Incorrect' would contradict established results derived by volume integration and universally referenced in engineering tables.

Common Pitfalls: Confusing the solid hemisphere with a hollow hemispherical shell; mixing the reference point (from base versus from the sphere centre).

Final Answer: Correct.