91Ó°ÊÓ

Density is a fundamental concept in physics that describes how compact a substance is. It's defined as mass per unit volume and is often represented by the Greek letter \( \rho \) (rho). You can calculate density using the formula:

• \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)
  

This means that density tells us how much matter exists in a given amount of space. In the context of floating bodies, understanding the density of both the floating object and the liquid it is in is crucial.

For a body to stay afloat, its density must be less than the density of the liquid. This principle is used daily in designing ships and understanding how various objects behave in water.

The buoyant force is an upward force exerted by a fluid, opposing the weight of an object that is either partially or fully immersed in it. This principle is central to understanding why some objects float and others do not. According to Archimedes' Principle,

• The buoyant force is equal to the weight of the fluid displaced by the object.

Mathematically, it is represented as:

• \( \text{Buoyant Force} = V \sigma g \)

where \( V \) is the volume of the fluid displaced, \( \sigma \) is the density of the fluid, and \( g \) is the acceleration due to gravity.

This force is what gives objects the ability to float. If the buoyant force is greater than or equal to the weight of the object, it will float. This is why heavier-than-water objects can still float if they displace enough water to equal their weight.

Apparent weight refers to the perceived weight of an object when it is submerged in a fluid, and it can change due to the buoyant force. When you're swimming or standing in water, you may notice that you feel lighter. This sensation is due to the buoyant force working against gravity.

For a floating object, the buoyant force is in perfect balance with the object's weight, resulting in an apparent weight of zero. Therefore, while a body is floating, it feels as if it doesn't weigh anything. This is why statement (c) in the exercise, which claims that the apparent weight is zero, is indeed correct.

Understanding apparent weight helps in designing things like ships and submarines, where balance and buoyancy are key considerations.

True weight is the actual weight of an object regardless of the medium around it. It is the force exerted by gravity on that object. The true weight can be calculated using the formula:

• \( \text{True Weight} = V \rho g \)

Here, \( V \) is the volume of the object, \( \rho \) is the object's density, and \( g \) is the acceleration due to gravity.

True weight is important for determining whether an object will float or sink when placed in a fluid. In the exercise, the true weight is part of the determining factor for the balance of forces responsible for the object's buoyancy. However, it's important to note that the true weight never changes while the object's apparent weight can vary based on its environment.