The specific gravity of ice is 0.9. The area of the smallest...

The specific gravity of ice is $0.9$. The area of the smallest slab of ice of height $0.5 \mathrm{~m}$ floating in fresh water that will just support a $100 \mathrm{~kg}$ man is
(A) $1.5 \mathrm{~m}^{2}$
(B) $2 \mathrm{~m}^{2}$
(C) $3 \mathrm{~m}^{2}$
(D) $4 \mathrm{~m}^{2}$

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Key Concepts

Maximum Load and Fully Submerged Condition

A floating body can only support additional weight until it becomes fully submerged. When the body is fully immersed, the maximum buoyant force is achieved, setting the limit for the load it can support without sinking. This concept is key when calculating load capacities in floating systems.

Specific Gravity and Density Relationships

Specific gravity is the ratio of the density of a substance to that of water. It helps determine the fraction of an object’s volume that is submerged when floating, as the submerged fraction is roughly equal to the ratio of the object's density to that of the fluid, influencing buoyant force calculations.

Archimedes’ Principle

This principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It is fundamental in determining how objects float and the conditions for equilibrium when additional loads are applied.

Buoyant Equilibrium of Floating Bodies

Floating bodies balance their weight against the buoyant force. For a floating slab, equilibrium occurs when the weight of the displaced water equals the combined weight of the slab and any additional load, which is essential for determining the maximum load the body can support.

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