A block of ice of area A and thickness 0.5 m is floating in the fresh water. In order to just s

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A block of ice of area A and thickness 0.5 m is floating in...

A block of ice of area $A$ and thickness $0.5 \mathrm{~m}$ is floating in the fresh water. In order to just support a man of 100 $\mathrm{kg}$, the area $A$ should be : (the specific gravity of ice is $0.917$ and density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ ) (a) $1.24 \mathrm{~m}^{2}$ (b) $4.21 \mathrm{~m}^{2}$ (c) $2.41 \mathrm{~m}^{2}$ (d) $7.23 \mathrm{~m}^{2}$

A block of ice of area $A$ and thickness $0.5 \mathrm{~m}$ is floating in the fresh water. In order to just support a man of 100 $\mathrm{kg}$, the area $A$ should be : (the specific gravity of ice is $0.917$ and density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ )
(a) $1.24 \mathrm{~m}^{2}$
(b) $4.21 \mathrm{~m}^{2}$
(c) $2.41 \mathrm{~m}^{2}$
(d) $7.23 \mathrm{~m}^{2}$

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Key Concepts

Archimedes Principle

Archimedes Principle is the foundational concept that states a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid that the body displaces. This principle is critical in problems dealing with floating or submerged objects, as it allows us to relate the object's weight and volume to the weight of the displaced fluid, ensuring equilibrium.

Buoyancy and Floating Equilibrium

Buoyancy refers to the upward force exerted by a fluid on an object immersed in it. A floating object is in equilibrium when the buoyant force (which equals the weight of the displaced fluid) exactly balances the object's weight. This concept is used to analyze how additional loads, like a man standing on a floating block, affect the submerged volume and overall equilibrium.

Density and Specific Gravity

Density is defined as mass per unit volume, and it helps relate mass changes to changes in volume. Specific gravity is the ratio of a substance's density to that of a reference substance, typically water. In floating problems, the specific gravity of a material (such as ice) is used to determine its density relative to water, which in turn influences the amount of fluid displaced and the resulting buoyant force.

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