A block of wood floats with 1 / 4 of its volume under water....

A block of wood floats with $1 / 4$ of its volume under water. What is the density of the wood? (Density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ ) (a) $750 \mathrm{~kg} / \mathrm{m}^{3}$ (b) $250 \mathrm{~kg} / \mathrm{m}^{3}$ (c) $300 \mathrm{~kg} / \mathrm{m}^{3}$ (d) $260 \mathrm{~kg} / \mathrm{m}^{3}$ $\mathbf{A 4}$

A block of wood floats with $1 / 4$ of its volume under water. What is the density of the wood? (Density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ )
(a) $750 \mathrm{~kg} / \mathrm{m}^{3}$
(b) $250 \mathrm{~kg} / \mathrm{m}^{3}$
(c) $300 \mathrm{~kg} / \mathrm{m}^{3}$
(d) $260 \mathrm{~kg} / \mathrm{m}^{3}$
$\mathbf{A 4}$

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Key Concepts

Archimedes’ Principle

This principle states that any object, wholly or partially immersed in a fluid, experiences an upward buoyant force equal to the weight of the fluid that is displaced by the object. It provides the foundation for understanding why objects float or sink based on their densities relative to the fluid.

Buoyancy and Equilibrium

For an object floating in equilibrium, the buoyant force must exactly balance its weight. This means that the weight of the displaced fluid is equal to the object's weight. This balance is crucial for determining how much of the object’s volume needs to be submerged, which in turn relates to the object's density.

Density

Density is defined as the mass per unit volume of a substance. In the context of floating objects, the ratio of the object’s density to the fluid's density determines the fraction of the object that is submerged. Knowing this relationship allows one to calculate the density of the floating object if the submerged fraction and the density of the fluid are known.

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