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A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow?
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A solid shell losses half of its weight in water , relative density of...
Calculating the Fraction of Hollow Volume in a Solid Shell
To determine the fraction of hollow volume in a solid shell, we need to consider its weight loss in water and its relative density.
Weight Loss in Water
When a solid object is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. In this case, the solid shell loses half of its weight in water. This means that the buoyant force acting on the shell when submerged in water is equal to half of its weight.
Relative Density
The relative density of a substance is the ratio of its density to the density of a reference substance. In this case, the relative density of the shell is given as 5. This means that the density of the shell is 5 times greater than the density of the reference substance, which is typically water.
Fraction of Hollow Volume
To calculate the fraction of hollow volume in the solid shell, we can use the concept of relative density.
1. Let's assume the original weight of the solid shell is W, and the weight loss in water is W/2.
2. Since the buoyant force acting on the shell is equal to half its weight, the buoyant force is W/2.
3. The buoyant force acting on the shell is also equal to the weight of the water displaced by the shell.
4. The volume of water displaced by the shell is given by the equation V_water = (W/2) / ρ_water, where ρ_water is the density of water.
5. The volume of the shell is given by V_shell = W / ρ_shell, where ρ_shell is the density of the shell.
6. The fraction of hollow volume in the shell can be calculated as the difference between the volume of the shell and the volume of water displaced, divided by the volume of the shell: (V_shell - V_water) / V_shell.
Explanation
The fraction of hollow volume in the solid shell can be calculated by subtracting the volume of water displaced by the shell from the volume of the shell, and then dividing the result by the volume of the shell. This fraction represents the portion of the shell's volume that is hollow.
By considering the weight loss in water and the relative density of the shell, we can determine the fraction of hollow volume in the shell.
To determine the fraction of hollow volume in a solid shell, we need to consider its weight loss in water and its relative density.
Weight Loss in Water
When a solid object is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. In this case, the solid shell loses half of its weight in water. This means that the buoyant force acting on the shell when submerged in water is equal to half of its weight.
Relative Density
The relative density of a substance is the ratio of its density to the density of a reference substance. In this case, the relative density of the shell is given as 5. This means that the density of the shell is 5 times greater than the density of the reference substance, which is typically water.
Fraction of Hollow Volume
To calculate the fraction of hollow volume in the solid shell, we can use the concept of relative density.
1. Let's assume the original weight of the solid shell is W, and the weight loss in water is W/2.
2. Since the buoyant force acting on the shell is equal to half its weight, the buoyant force is W/2.
3. The buoyant force acting on the shell is also equal to the weight of the water displaced by the shell.
4. The volume of water displaced by the shell is given by the equation V_water = (W/2) / ρ_water, where ρ_water is the density of water.
5. The volume of the shell is given by V_shell = W / ρ_shell, where ρ_shell is the density of the shell.
6. The fraction of hollow volume in the shell can be calculated as the difference between the volume of the shell and the volume of water displaced, divided by the volume of the shell: (V_shell - V_water) / V_shell.
Explanation
The fraction of hollow volume in the solid shell can be calculated by subtracting the volume of water displaced by the shell from the volume of the shell, and then dividing the result by the volume of the shell. This fraction represents the portion of the shell's volume that is hollow.
By considering the weight loss in water and the relative density of the shell, we can determine the fraction of hollow volume in the shell.
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A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow?
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A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow?.
A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid shell losses half of its weight in water , relative density of shell is 5. What fraction of its volume is hollow?.
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