Determining the Relative Density of a Solid Using Weight Loss in Water

Understanding the concept of relative density (or specific gravity) is crucial in various scientific and engineering applications. This process involves determining the ratio of the density of a substance to the density of a reference substance, usually water. Let's explore a common problem where a solid weighing 20 N in air is dipped in water and its apparent weight is measured as 18 N. We will use this to calculate the relative density of the solid.

Understanding Relative Density and Water Displacement

The apparent weight loss of a submerged body in water is equal to the weight of the water it displaces. This principle is fundamental in fluid mechanics and is used to understand the buoyant force acting on an object.

Calculating the Weight of Displaced Water

In the given scenario, a solid originally weighs 20 N in air but when dipped in water, it weighs only 18 N. The difference in weight represents the weight of the water displaced by the solid. Therefore:

[ text{Weight of the solid in water} 18 text{ N} ] [ text{Weight lost} 20 text{ N} - 18 text{ N} 2 text{ N} ]

This 2 N represents the weight of the water displaced by the solid. Since 1 N corresponds to approximately 100 grams in air, the weight of the displaced water is:

[ 2 text{ N} approx 200 text{ grams} ]

Volume of Displaced Water

The volume of the displaced water can be calculated using the density of water, which is approximately 1000 kg/m3. The volume of water displaced is:

[ text{Volume of displaced water} frac{text{Mass of displaced water}}{text{Density of water}} frac{200 text{ grams}}{1000 text{ kg/m}^3} 0.2 text{ liters} approx 200 text{ cm}^3 ]

Volume of the Solid

Since the solid displaces a volume of water equivalent to its own volume, the volume of the solid is:

[ text{Volume of the solid} 200 text{ cm}^3 ]

Calculating the Density of the Solid

The density of the solid can be calculated using its mass and volume. The mass of the solid is given as 20 grams. Therefore:

[ text{Density of the solid} frac{text{Mass of the solid}}{text{Volume of the solid}} frac{20 text{ grams}}{200 text{ cm}^3} 0.1 text{ g/cm}^3 text{ or } 10 text{ g/cm}^3 ]

Relative Density (Specific Gravity) Calculation

The relative density (specific gravity) of the solid is the ratio of the density of the solid to the density of water:

[ text{Relative density} frac{text{Density of the solid}}{text{Density of water}} frac{10 text{ g/cm}^3}{1 text{ g/cm}^3} 10 ]

Summary

To summarize, we determined that the solid has a relative density (specific gravity) of 10. This means the solid is 10 times denser than water. Understanding this concept is essential for various applications in science and engineering, such as calculating buoyancy and density.

Precautions and Advice

Remember that websites like Quora are not intended as homework help. If you need assistance with a problem, it's best to guide yourself through the steps and seek help from educational resources or mentors, rather than asking for direct answers. This approach helps in reinforcing your learning and understanding.

Keep practicing similar problems to enhance your problem-solving skills. The more you practice, the more intuitive and simple these concepts will become.