Floatation in Liquids

Floatation in Liquids

Buoyant Force

When a body is immersed partly or wholly in a liquid, a force acts on the body by the liquid in the upward direction. This force is called the Buoyant force or the force of buoyancy or upthrust. It is equal to the weight of liquid displaced by the body and acts at the centre of gravity of the displaced liquid. Its study was first made by Archimedes.

Archimedes Principle

• When a body is immersed partly or wholly in a liquid, there is an apparent loss in the weight of the body which is equal to the weight of the liquid displaced by the body.

Law of Floatation

• A body floats in a liquid if:

1. The density of the material of the body is less than or equal to the density of the liquid.

2. If the density of the material of the body is equal to the density of the liquid, the body floats fully submerged in the liquid in neutral equilibrium.

3. When the body floats in neutral equilibrium, the weight of the body is equal to the weight of displaced liquid.

4. The centre of gravity of the body and the centre of gravity of the displaced liquid should be in one vertical line.

Centre of Buoyancy

The centre of gravity of the liquid displaced by a body is called the centre of buoyancy.

Metacentre

• When a floating body is slightly tilted from equilibrium, the center of buoyancy shifts. T

• The point at which the vertical line passing through the new position of the center of buoyancy meets the initial line is called the metacentre.

Effects of Floating and Immersed Bodies

• When a solid body is dropped from a boat floating in water:

  • Falls if the density of the solid > density of water.

  • Remains unchanged if the density of the solid < density of water.

• When a piece of ice floating in liquid melts completely, the level of liquid:

  1. Remains unchanged if the density of liquid = the density of water.

  2. Falls if the density of the liquid < density of water.

  3. Rises if the density of the liquid > density of water.

• When a solid embedded in ice melts:

  • Falls if the density of the solid > density of water.

  • Does not change if the density of the solid < density of water.

• If passengers in a boat floating in a tank drink water from the tank, the water level does not change.

Conditions for Stable Equilibrium of a Floating Body

1. The metacentre must always be higher than the centre of gravity of the body.

2. The line joining the centre of gravity of the body and the centre of flotation should be vertical.

Mass

• The amount of substance contained in a body is called its mass.

• Mass is a constant quantity. It does not change like weight.

Density

Density is defined as mass per unit volume.

• SI unit: kg/m³

• Relative density = density of material ÷ density of water at 4°C

• Since relative density is a ratio, it is unitless.

• Relative density is measured by a hydrometer.

Examples and Applications:

• The density of seawater is more than normal water, making it easier to swim in seawater.

• When ice floats in water, 1/10th part remains outside the water.

• If floating ice melts in a vessel, the water level does not change.

• Purity of milk is measured by a lactometer.

Final Thoughts

Buoyant force is the upward force a liquid exerts on a body, equal to the weight of liquid displaced, as discovered by Archimedes. According to Archimedes’ Principle, a body loses apparent weight equal to the displaced liquid. A body floats if its density is less than or equal to the liquid, and in neutral equilibrium, its weight equals the weight of displaced liquid.

The center of buoyancy and metacentre determine stability when a body tilts. Everyday examples include boats, floating ice, and water tanks, while mass remains constant and density is measured by a hydrometer.

Relative density explains why swimming in seawater is easier, and instruments like lactometers check milk purity.