To find the density of a body heavier than water by Archimedes principle

 

Abstract

This experiment aims to determine the density of a body heavier than water using Archimedes' principle. By measuring the apparent weight loss of the body when immersed in water, the volume of the body can be calculated and used to find its density.

Introduction

Archimedes' principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. In this experiment, we utilize this principle to find the density of a body that is heavier than water. By measuring the apparent weight loss of the body when immersed in water, we can determine its volume and subsequently calculate its density.

Procedure

1. Measure the mass (\( m \)) of the body using a balance.
2. Fill a container with water and measure its mass (\( m_w \)) using a balance.
3. Suspend the body from a spring balance and measure its weight (\( W \)) in air.
4. Immerse the body fully in the water and measure its apparent weight (\( W' \)).
5. Calculate the apparent loss of weight (\( \Delta W \)) using the formula: \( \Delta W = W - W' \).
6. Calculate the volume (\( V \)) of the body displaced by water using Archimedes' principle: \( V = \frac{{\Delta W}}{{\text{Density of water}}} \).
7. Calculate the density (\( \rho \)) of the body using the formula: \( \rho = \frac{m}{{V}} \).

Observations and Calculations

Assume the following observations were made during the experiment:

• Mass of the body (\( m \)): 150 g
• Mass of water (\( m_w \)): 500 g
• Weight of the body in air (\( W \)): 15 N
• Apparent weight of the body in water (\( W' \)): 12 N
• Density of water: \( 1000 \, \text{kg/m}^3 \)

Using the given data, we can calculate the apparent loss of weight (\( \Delta W \)) and the volume (\( V \)) of the body. Then, we can find its density (\( \rho \)) using the formula mentioned above.

Conclusion

The experiment successfully demonstrates the use of Archimedes' principle to find the density of a body heavier than water. By measuring the apparent loss of weight when immersed in water, we can accurately determine the volume of the body and calculate its density.

Precautions

• Ensure the body is fully submerged in water without touching the sides or bottom of the container.
• Handle the body and equipment carefully to avoid errors or accidents.
• Take accurate measurements of mass and weight using calibrated instruments.
• Repeat the experiment multiple times to ensure consistency and reliability of results.

Short Questions with Answers

1. What is Archimedes' principle?
   Answer: It states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object.
2. How is Archimedes' principle used to find the density of a body?
   Answer: By measuring the apparent loss of weight when the body is immersed in water.
3. What is the significance of measuring the mass of the displaced water?
   Answer: It helps in calculating the volume of the body displaced by water.
4. What factors affect the accuracy of the experiment?
   Answer: Accurate measurements of mass, weight, and volume, as well as proper immersion of the body in water.
5. What precautions should be taken while suspending the body in water?
   Answer: Ensure the body is fully submerged and does not touch the sides or bottom of the container.
6. Why is it important to measure the weight of the body in air?
   Answer: To determine the apparent loss of weight when the body is immersed in water.
7. What is the formula for calculating the apparent loss of weight?
   Answer: \( \Delta W = W - W' \), where \( \Delta W \) is the apparent loss of weight, \( W \) is the weight of the body in air, and \( W' \) is the apparent weight of the body in water.
8. What does the density of water need to be known for?
   Answer: To calculate the volume of the body displaced by water.
9. What happens if the body is not fully submerged in water?
   Answer: The volume of the body displaced by water will be inaccurately measured, leading to errors in density calculation.
10. What is the SI unit of density?
    Answer: Kilograms per cubic meter (kg/m³).
11. How can the density of a body be calculated using Archimedes' principle?
    Answer: By dividing the mass of the body by the volume of water displaced by it.
12. What happens to the buoyant force when a body is immersed in water?
    Answer: It increases, equaling the weight of the water displaced by the body.
13. What does a higher apparent loss of weight indicate?
    Answer: It indicates a greater volume of water displaced by the body, which corresponds to a higher density.
14. Why is it important to ensure the body is completely dry before weighing?
    Answer: Any water adhering to the body would increase its apparent weight in water, leading to errors in the experiment.
15. What is the purpose of repeating the experiment multiple times?
    Answer: To ensure the reliability and consistency of the results.
16. How can the volume of water displaced by the body be measured?
    Answer: By measuring the mass of water displaced and dividing it by the density of water.
17. What happens if the body sinks to the bottom of the container?
    Answer: It displaces a volume of water equal to its own volume.
18. What precautions should be taken to avoid errors in mass measurements?
    Answer: Ensure the balance is properly calibrated and the body is placed gently on the balance pan.
19. What is the expected outcome if the body has a density greater than that of water?
    Answer: The body will sink when immersed in water.
20. What is the role of the container in the experiment?
    Answer: It holds the water and provides a stable environment for the immersion of the body.

Multiple-Choice Questions (MCQs)

1. What is the principle used in this experiment?
   A) Pascal's Law
   B) Bernoulli's Principle
   C) Archimedes' Principle
   D) Newton's Third Law
   Correct Answer: C) Archimedes' Principle
2. How is the volume of the body determined in this experiment?
   A) By measuring its mass
   B) By measuring its weight
   C) By measuring the displacement of water
   D) By measuring its density
   Correct Answer: C) By measuring the displacement of water
3. What is the density of water typically?
   A) 1 g/cm³
   B) 100 kg/m³
   C) 1000 kg/m³
   D) 10 g/cm³
   Correct Answer: C) 1000 kg/m³
4. Why is it important to measure the apparent loss of weight?
   A) To determine the density of the body
   B) To determine the volume of the body
   C) To calculate the buoyant force
   D) To calculate the mass of the body
   Correct Answer: B) To determine the volume of the body
5. What happens if the body is not fully submerged in water?
   A) The apparent loss of weight will be inaccurate
   B) The volume of the body will be overestimated
   C) The experiment cannot be performed
   D) The body will float on the surface of the water
   Correct Answer: B) The volume of the body will be overestimated