Archimedes' Principle and Buoyancy - UNSOLVED PRACTICE SET
Chapter: Mechanical Properties of Fluids | Topic: Archimedes Principle and Buoyancy
ARCHIMEDES' PRINCIPLE AND BUOYANCY - UNSOLVED PRACTICE SET
Topic: Archimedes Principle and Buoyancy
Multiple Choice Questions
Q1. Archimedes' principle states that the buoyant force on a body immersed in a fluid is equal to:
- The weight of the body
- The weight of the fluid displaced by the body
- The volume of the body
- The density of the body
Q2. A body floats in a liquid when:
- Its density is greater than the liquid
- Its density is less than the liquid
- Its weight is greater than the buoyant force
- Its volume is less than the liquid displaced
Q3. The apparent weight of a body immersed in a liquid is:
- Greater than its actual weight
- Less than its actual weight
- Equal to its actual weight
- Zero
Q4. A ship made of iron floats because:
- Iron is lighter than water
- The average density of the ship (including air spaces) is less than water
- The ship displaces less water than its weight
- Iron expands in water
Q5. When a body is completely immersed in a liquid, the buoyant force depends on:
- The mass of the body
- The volume of the body
- The density of the body
- The shape of the body
Q6. The law of flotation states that a floating body displaces:
- A volume of liquid equal to its own volume
- A weight of liquid equal to its own weight
- A volume of liquid equal to half its own volume
- A weight of liquid equal to half its own weight
Short Answer Questions
Q7. State Archimedes' principle. Explain why the buoyant force acts vertically upward.
Q8. A body weighs 50 N in air and 40 N when immersed in water. Calculate the buoyant force and the volume of the body.
Q9. Why does an iron nail sink in water while a ship made of iron floats?
Q10. In your school, a student places an ice cube in a glass of water. The ice floats with part of it above water. Explain why, and what happens when the ice melts.
Q11. A solid weighs 100 N in air, 80 N in water, and 60 N in a liquid. Calculate the relative density of the liquid.
Q12. Explain why it is easier to swim in sea water than in fresh water.
Long Answer Questions
Q13. State and prove Archimedes' principle. Explain the concept of buoyant force and derive its expression. Discuss the conditions for floating, sinking, and neutral buoyancy with examples.
Q14. A wooden block of density 600 kg/m³ and volume 0.02 m³ is floating in water.
(a) Calculate the weight of the block.
(b) Calculate the volume of water displaced.
(c) Calculate the fraction of the block above water.
(d) What minimum force is required to completely submerge the block?
(e) If the block is placed in oil of density 800 kg/m³, what fraction remains above the oil?
Q15. Analyse the following situations using Archimedes' principle:
(i) A hot air balloon rising
(ii) A submarine diving and surfacing
(iii) A hydrometer measuring liquid density
For each case, explain:
(a) The physics involved
(b) How the principle is applied
(c) Practical considerations and limitations
Application-Based Problems
Q16. A metal sphere of radius 5 cm and density 8000 kg/m³ is completely immersed in water.
(a) Calculate the volume of the sphere.
(b) Calculate the buoyant force on the sphere.
(c) Calculate the apparent weight of the sphere in water.
(d) The sphere is now suspended by a string from a spring balance. What does the balance read?
(e) If the sphere is hollow with an internal cavity of volume 400 cm³, will it float or sink? Calculate the new apparent weight.
Q17. A boat floating in a lake carries a large rock.
(a) The rock is thrown overboard. Does the water level in the lake rise, fall, or remain the same? Explain.
(b) Calculate the change in water level if the rock has mass 100 kg and density 5000 kg/m³. (Lake area = 1000 m²)
(c) If the rock were made of ice instead and it melts, what happens to the water level?
(d) A person in the boat drinks some water from the lake. Does the water level change?
(e) Discuss the principle behind designing life jackets.
Q18. In a school experiment, students determine the density of an irregular stone using Archimedes' principle.
(a) Describe the experimental procedure step by step.
(b) The stone weighs 2.5 N in air and 1.5 N in water. Calculate its density.
(c) The same stone is weighed in a salt solution and reads 1.6 N. Calculate the density of the salt solution.
(d) Why must the stone be completely immersed but not touching the bottom?
(e) Suggest two sources of error in this experiment and how to minimise them.