Liquid at Rest | Jamb(UTME)

Determination of Density of Solids and Liquids

1. Density is the mass per unit volume of a substance and is given by:
   
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   $\text{Density} = \frac{Mass}{Volume}$
2. The unit of density in the SI system is kilograms per cubic meter (kg/m³).
3. For solids, density is determined by measuring the mass using a balance and the volume by geometric calculations.
4. For irregular solids, volume is measured using the water displacement method.
5. In the water displacement method, the volume of water displaced equals the volume of the object.
6. The mass of liquids is measured using a balance and a container, subtracting the container’s mass.
7. The volume of liquids is measured using a graduated cylinder or measuring beaker.
8. The density of a liquid is found by dividing its mass by its volume.
9. The density of solids or liquids can also be determined using a hydrometer (for liquids) or a density bottle.
10. Comparing densities helps determine whether substances float or sink in a fluid.
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Definition of Relative Density

11. Relative density is the ratio of the density of a substance to the density of water.
12. It is a dimensionless quantity (no unit).
13. Relative density is given by:
    
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    ${Relative Density}$ = $\frac{Density of Substance}{Density of Water}$
14. Water has a density of approximately $1000kg$/$m^3$ at standard conditions.
15. A relative density greater than 1 means the substance is denser than water and will sink.
16. A relative density less than 1 means the substance is less dense than water and will float.
17. Relative density helps in identifying substances and their purity.
18. It is widely used in industries like mining, petroleum, and shipping.
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Upthrust on a Body Immersed in a Liquid

19. Upthrust, or buoyant force, is the upward force exerted by a fluid on a submerged or floating object.
20. Upthrust occurs because the pressure at the bottom of an object in a fluid is greater than at the top.
21. The magnitude of upthrust depends on the volume of fluid displaced by the object.
22. Upthrust is responsible for objects floating in water or sinking to a certain depth.
23. The formula for upthrust is:
    
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    **Upthrust = Weight of Displaced Fluid
24. If the upthrust equals the object's weight, the object floats.
25. If the upthrust is less than the object's weight, the object sinks.
26. Upthrust explains why heavy ships can float despite their large mass.
27. The greater the density of the liquid, the higher the upthrust it exerts.
28. Submarines adjust their buoyancy by controlling the volume of water in ballast tanks.
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Archimedes’ Principle

29. Archimedes' principle states that a body partially or fully immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced.
30. The principle applies to both liquids and gases.
31. Archimedes' principle is mathematically expressed as:
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    ${Upthrust} = {Density of Fluid} \times {Volume Displaced} \times g$
32. This principle explains why objects float, sink, or remain suspended in a fluid.
33. Archimedes' principle is used in designing ships, submarines, and floating devices.
34. It helps determine the volume and density of irregularly shaped objects.
35. The principle is crucial in understanding the behavior of hydrometers and fluid displacement.
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Law of Floatation

36. The law of floatation states that a floating object displaces a weight of fluid equal to its own weight.
37. For an object to float, the density of the object must be less than or equal to the density of the fluid.
38. The part of the object submerged in the fluid displaces a volume of fluid equal to the object's weight.
39. Large objects, like ships, float because their overall density (including air spaces) is less than water.
40. The shape and design of floating objects ensure stability and sufficient buoyancy.
41. The law of floatation is widely used in marine engineering and shipbuilding.
42. Icebergs float in the ocean because their density is less than seawater.
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Applications: Ships and Hydrometers

Ships

43. Ships float because their design ensures they displace enough water to balance their weight.
44. The hull of a ship is designed to trap air, reducing its overall density.
45. Large cargo ships are built with compartments to maintain stability even when carrying heavy loads.
46. Archimedes' principle and the law of floatation are critical in ensuring a ship remains buoyant.
47. Submarines dive and surface by controlling their density through ballast tanks.
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Hydrometers

48. A hydrometer is a device used to measure the relative density of liquids.
49. Hydrometers float in a liquid, with the level of immersion indicating the liquid's density.
50. Hydrometers are used in industries to check the purity of liquids, measure alcohol content, or monitor battery acid density.
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