Buoyancy And Floatation

Step 1: Understanding the problem.
The weight of the hollow metallic sphere in air is 264 gm-wt, and in water, it is 221 gm-wt. The difference in weight is due to the buoyant force, which is equal to the weight of the water displaced by the volume of the hollow portion of the sphere. The buoyant force is:
Step 2: Using Archimedes' principle.
The buoyant force is also
given by the equation:
where is the density of water, is the volume of the hollow portion, and is the acceleration due to gravity. Since the specific gravity of the metal is 8.8, the volume of the hollow portion can be calculated as: Thus, the correct answer is
(B) 12 cm
.