Define floating body.

Short Answer:

A floating body is a solid object that partly remains above and partly below the surface of a fluid, such as water, due to the upward buoyant force acting on it. The buoyant force balances the weight of the body, allowing it to float at a certain level.

In simple words, when a body floats, it displaces a volume of fluid whose weight equals the body’s weight. Examples of floating bodies include ships, boats, icebergs, and wooden logs. The stability of a floating body depends on the positions of its center of gravity and center of buoyancy.

Detailed Explanation :

Floating Body

A floating body is defined as a solid body that remains partially submerged in a fluid, with a part of it above the fluid surface and a part below. This happens when the upward buoyant force exerted by the fluid equals the downward weight of the body. The condition of floating depends on the density of the body compared to the density of the fluid.

According to Archimedes’ Principle, the buoyant force acting on a body is equal to the weight of the fluid displaced by the submerged portion of the body. Hence, when a body floats, the amount of fluid displaced is such that its weight equals the weight of the floating body itself.

Mathematically,

\text{Weight of the body (W)} = \text{Buoyant force (F_B)}

That is,

Where,

  •  = Density of the body
  •  = Total volume of the body
  •  = Density of the fluid
  •  = Submerged volume of the body
  •  = Acceleration due to gravity

The body floats when the density of the body is less than or equal to the density of the fluid.

Condition for Floating

The condition for a body to float in a fluid is derived from the balance of forces acting on it.

  1. Buoyant Force (F_B):
    • It acts vertically upward through the center of buoyancy (B), which is the centroid of the displaced fluid volume.
  2. Weight of the Body (W):
    • It acts vertically downward through the center of gravity (G) of the body.

For floating condition,

Therefore,

Simplifying,

This ratio   represents the fraction of the body submerged in the fluid.

  • If  , the body floats partially submerged.
  • If  , the body remains fully submerged (neutral floating).
  • If  , the body sinks.

Forces Acting on a Floating Body

When a body floats in a fluid, two main forces act on it:

  1. Weight (W):
    • Acts vertically downward through the center of gravity (G) of the body.
  2. Buoyant Force (F_B):
    • Acts vertically upward through the center of buoyancy (B).

For equilibrium, these two forces must be equal in magnitude and opposite in direction.

However, for the floating body to remain stable, the metacenter (M), center of gravity (G), and center of buoyancy (B) must maintain proper relative positions.

Stability of Floating Body

The stability of a floating body determines whether it will remain upright or topple when disturbed.

  1. Stable Equilibrium:
    • When the metacenter (M) lies above the center of gravity (G).
    • The body returns to its original position after being tilted.
    • Example: A well-balanced ship on water.
  2. Neutral Equilibrium:
    • When the metacenter (M) coincides with the center of gravity (G).
    • The body remains in the new position after tilting.
  3. Unstable Equilibrium:
    • When the metacenter (M) lies below the center of gravity (G).
    • The body overturns when slightly disturbed.
    • Example: A tall, narrow boat with heavy top weight.

Thus, for a floating body to be stable, it should have a low center of gravity (G) and a high metacenter (M).

Examples of Floating Bodies

  1. Ship:
    A ship floats because its average density (metal + air inside) is less than that of water. It displaces a large amount of water to balance its weight.
  2. Boat:
    A boat floats for the same reason — the air inside reduces its average density compared to water.
  3. Iceberg:
    Icebergs float because the density of ice is less than that of seawater. About 90% of an iceberg is submerged, and only 10% is visible above the water.
  4. Wooden Log:
    A piece of wood floats in water because its density is less than that of water.
  5. Hydrometer:
    A hydrometer floats partially in a liquid, and the level to which it sinks depends on the liquid’s density.

Mathematical Example

A wooden block of volume   has a density of  . Determine the fraction of the block submerged when it floats on water ( ).

Given:

 

Hence, 60% of the block is submerged in water while 40% remains above the surface.

Applications of Floating Body Concept

  1. Ship and Boat Design:
    • Used in marine engineering to ensure stability and buoyancy.
  2. Submarines:
    • Designed using buoyancy control to float or submerge as needed.
  3. Buoys and Floating Docks:
    • Used for marine navigation and offshore platforms.
  4. Hydrometer Construction:
    • Based on floating principles to measure fluid density.
  5. Engineering Safety:
    • Ensures that floating machines and equipment do not capsize.
Conclusion

In conclusion, a floating body is one that remains partly submerged in a fluid due to the balance between its weight and the buoyant force exerted by the fluid. The amount of the body submerged depends on its density relative to the fluid’s density. The stability of the floating body depends on the positions of its center of gravity and metacenter. This concept is widely applied in designing ships, boats, and submarines to ensure that they float safely and remain stable on the water surface.