Buoyancy and Floatation MCQ with answer and solution

Concept

Centre of buoyancy = centroid of the displaced volume

Formula

Centroid of a cone from its apex = 3/4 × height

Step-by-step solution

1. The displaced liquid has the shape of a cone of height h with its apex at the bottom (apex of the floating cone). 2. The centroid of a solid cone lies at 3/4 of its height from the apex. 3. So the centre of buoyancy is 3h/4 above the apex.

Explanation

The centre of buoyancy is the centroid of the volume of liquid displaced. The submerged part of the cone is itself a cone with height h, so its centroid is 3h/4 from the apex (h/4 from the base).

Shortcut

Solid cone centroid: h/4 from base. Triangle centroid: h/3 from base. Hemisphere: 3R/8 from base.

Common mistake

Using 2h/3 (centroid of a triangular area) instead of 3h/4 (solid cone).