Floating Bodies

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Usually, all bodies less than that of water float, bodies which are denser than water sink. You might have noticed that a piece of steel sinks, but a ship made of steel floats. This is because of the design of the ship. The steel body of the ship encloses large quantity of air. Thus, the average density of the ship is less than that of water and the ship floats in water.

Law of Flotation

When a floating body like wood is placed in water, it sinks until the weight of water displaced by it is just equal to its own weight and then it floats. This leads us to the principle of floatation.

Principle of Floatation

A floating body displaces an amount of fluid equal to its own weight.

Plimsol Line

A ship sinks in water until its weight is equal to the upthrust on it. This upthrust is the weight of the water displaced by the submerged part of the ship.

The density of the sea varies in different parts of the world. This is due to the mineral salts dissolved in sea water as well as the variation in the temperature due to the climatic conditions. Hence, a ship sinks to different levels if its journey takes it to different regions. When a ship sinks too low in water it is unsafe in heavy seas, and the danger increases if the cargo carried is very heavy. In the 19^th century Plimsol agitated for the safety of ships, as a result certain standard levels upto which a ship can be allowed to submerge in different waters were evolved. These are marked on the side of ships and are known as the Plimsol line.

It is now illegal for a ship to be loaded such that the 'Plimsol line' is below the water level. Figure below illustrates these markings.

Plimsol line

Floating and Sinking

When an object is placed on the surface of a liquid it will either float or sink. This depends upon two forces:

• The weight W₁ acting vertically downwards, which is due to the gravitational pull of the earth, and

• Upthrust or buoyant force acting vertically upwards, which is equal to the weight of the liquid displaced by the object W₂.

You know that the weight of an object is the product of its volume and its density. Hence,

W₁ = Volume of the object (V) x Density of the object (d₁)

W₂ = Volume of the liquid displaced (V) x Density of the liquid (d₂)

Let us see what are the different situations under which a body floats, sinks or remains submerged completely at any level in the liquid.

Case 1:

When the weight of the object W₁ is equal to the weight of the liquid displaced W₂, the object will stay in the position of rest completely immersed in the liquid. Here,

W₁ = W₂ or

V x d₁ = V x d₂ or d₁ = d₂, then the object will be floating completely immersed in a liquid as shown in figure below.

Weight of the object is equal to the weight of the liquid

Case 2:

When the weight of the object is greater than the weight of the displaced liquid, the object will sink. Here,

Thus, when the density of the object is greater than the density of the liquid, the object will sink.

Weight of the object is greater than the weight of the liquid displaced.

Case 3:-

When the weight of the object is less than the buoyant force (upthrust), the object will float on the surface of the liquid.

When the object floats, only a part of it is submerged in the liquid and volume of the liquid displaced will be less than its own volume. Let V' be the volume of the liquid displaced by the submerged part of the object. Here

Density of the solid is less than the density of the liquid and hence the object will float.

Weight of the object is less than the weight of the liquid displaced