NCERT Class 9 Science — Chapter 3: Gravitation

Correct Option

The correct option is

The weight of the fluid displaced by the body.

Explanation

Archimedes’ Principle is a fundamental law of fluid mechanics that governs the buoyancy of objects. It relates the upward force exerted on a submerged or floating object to the amount of fluid it displaces.

Detailed Analysis

• Statement of the Principle: Archimedes’ Principle states that when a body is immersed fully or partially in a fluid at rest, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by the body.
• Mathematical Representation:
  Buoyant Force ($F_B$) = Weight of displaced fluid ($W_{fluid}$)
  $F_B = \text{mass of fluid} \times g = (\text{density of fluid} \times \text{volume of fluid displaced}) \times g$
• Analysis of Options:
  • The weight of the body.: Incorrect. The buoyant force equals the weight of the body only if the body is floating (Law of Floatation). If the body sinks, its weight is greater than the buoyant force.
  • The volume of the fluid displaced.: Incorrect. Volume is a measure of space occupied, not a force. While the volume of the displaced fluid determines the magnitude of the force, it is not the force itself.
  • The weight of the fluid displaced by the body.: Correct. This is the direct definition of Archimedes’ Principle. The upward force is exactly equal to the gravitational force acting on the displaced fluid mass.
  • The density of the fluid displaced.: Incorrect. Density is an intrinsic property of the fluid, not a force.

Key Takeaway

Buoyant Force depends on the density of the fluid and the volume of the submerged part of the body. It is always equal to the weight of the fluid displaced, regardless of the weight of the object itself.