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Density is an important property of fluids that influences how objects behave when submerged. It is defined as the mass of a substance per unit volume, denoted by the symbol \( \rho \). The formula for density is \( \rho = \frac{M}{V} \), where \( M \) is the mass and \( V \) is the volume.

Understanding the density of water is crucial when dealing with problems involving buoyancy, such as this exercise. Water has a density approximately equal to 1000 kg/m³. This means a cubic meter of water weighs about 1000 kilograms.

In this exercise, the ball floats because it is less dense than water. Only 24% of its volume is submerged while in equilibrium. This fraction allows us to determine the relationship between the ball’s density and the water's density.

Knowing the density of the fluid helps determine the buoyant force acting on submerged objects. If you know the density of another fluid, you can predict whether the object will float or sink.

The volume of a submerged object is key in calculating the buoyant force it experiences. For an object floating in a fluid, the volume of the submerged portion of the object is equal to the volume of the fluid displaced.

In the given problem, 24% of the plastic ball's volume is submerged while it floats. This means that the displacement of water accounts for 24% of the ball's total volume. You can calculate the volume of the ball using the formula for the volume of a sphere: \[ V = \frac{4}{3}\pi r^3 \]where \( r \) is the radius of the ball. This gives insight into how much of the ball sits below the water's surface.

When an object is completely submerged, as in this problem when we push the ball below the surface, the entire volume of the object displaces an equal volume of fluid. This is critical for calculating the buoyant force when the ball is completely underwater. This approach helps predict how submerged objects behave under different conditions.

Newton's Second Law of Motion is a principle that explains how the velocity of an object changes when it is subject to an external force. It is succinctly expressed as \( F = ma \), where \( F \) is the force applied, \( m \) is the mass of the object, and \( a \) is the acceleration.

In the context of our exercise, this law helps determine how the ball behaves when it is released from below the water's surface. Upon release, the forces acting on the ball include the buoyant force and the gravitational force (weight of the ball).

The net force acting on the ball is the difference between the buoyant force and its weight. Since the buoyant force is greater when the ball is fully submerged, the net force becomes upward, leading to acceleration. By rearranging Newton's Second Law, we find the ball's acceleration as:\[ a = \frac{F}{m} \]where \( F \) is the net force (buoyant force minus gravitational force), and \( m \) is the mass of the ball.

This principle allows us to predict and quantify the ball's motion as it moves upward through the water, offering insights into the dynamics of submerged objects.