Body floats in fluid when its …………………

Analysis of the Question

This question tests your understanding of Archimedes' Principle and the Law of Flotation. To solve this, we need to look at the forces acting on a body that is floating in a fluid.

Concept Explanation

When a body is placed in a fluid, two main vertical forces act on it:

1. Weight ($W$): The downward force due to gravity acting on the body.
2. Upthrust ($U$): The upward force exerted by the fluid on the body.

According to Archimedes' Principle, the upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

For a body to float (stay in equilibrium without sinking or rising), the downward force must exactly balance the upward force. Therefore:

• Weight of the body = Upthrust
• Since Upthrust = Weight of the fluid displaced, it follows that:
• Weight of the body = Weight of the fluid displaced

Step-by-Step Solution

1. Identify the condition for floating: A body floats when it is in equilibrium.
2. Apply the Law of Flotation: The Law of Flotation states that a floating body displaces its own weight of the fluid in which it floats.
3. Evaluate the options: • Option A is incorrect because a body only displaces its own volume if it is fully submerged. • Option B aligns perfectly with the Law of Flotation. • Option C is physically incorrect as you cannot displace "density." • Option D is incorrect because gravity is always acting on the body; it is the balance of forces that keeps it floating, not the absence of gravity.

Conclusion

The correct condition for a body to float is that it must displace a volume of fluid whose weight is equal to the weight of the body itself.

Exam Tip: Always remember the phrase: "A floating body displaces its own weight." If the question asked about a submerged body, the answer would be that it displaces its own volume. Don't mix these two up in the exam hall!