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At its core, fluid mechanics is the branch of physics concerned with the behavior of fluids鈥攍iquids and gases鈥攁nd the forces on them. It has wide applications, extending from everyday household tasks to sophisticated engineering designs. In our exercise, fluid mechanics concepts allow us to predict how water will exert force on a submerged object, like the rubber ball.

When an object is immersed in a fluid, it feels an upward force because the pressure at the bottom of the object is greater than the pressure at the top. This disparity is due to the depth-dependent nature of fluid pressure; deeper in the fluid, the pressure increases. This fundamental understanding provides us the tools to analyze the rubber ball鈥檚 behavior in water and is essential in calculating the force needed to keep it submerged in equilibrium.

Buoyancy is the uplifting force that a fluid exerts on any object submerged in it. The principle of buoyancy is crucial in understanding why some objects float while others sink. This concept is tightly connected to the density of objects in comparison to the fluid they are in. A solid understanding of buoyancy is not just important for solving problems in physics but also in real-life scenarios such as designing ships or understanding the science behind swimming.

In our exercise, the rubber ball has a lower density compared to the water, due to which it experiences an upward buoyant force. To calculate this force, which we often call the 'buoyant force', we must know the volume of water displaced by the ball. This concept is directly linked to Archimedes' principle and is calculated based on the volume of the submerged part of the object.

Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. This principle is a gateway to understanding why ships float and balloons rise in the air. It's one of the fundamental principles used in hydrostatics鈥攖he study of fluids at rest鈥攁nd is derived from the observations made by the ancient Greek mathematician and inventor, Archimedes.

Based on this principle, in the step-by-step solution, the buoyant force on the rubber ball is precisely the weight of the volume of water it displaces. In mathematical terms, for the ball in equilibrium, the buoyant force must counterbalance the weight of the ball, which leads us to the calculation seen in the problem. For the ball to be in equilibrium, the upward buoyant force must exactly balance the downward force of gravity on the ball鈥攁 beautiful illustration of how physical concepts interplay to provide a detailed understanding of phenomena encountered in everyday life.