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Physics

Principle of Archimedes

Chapter: Properties of Matter

Question 1 of 3 NDA MCQ

 All objects experience a buoyancy when theyare immersed in a fluid. Buoyancy is

Detailed Explanation

Correct Answer

✓ Option (c) is correct. Buoyancy is an upward force acting on objects in a fluid.

📖 Governing Law / Core Concept

According to Archimedes' Principle, any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

🧪 Step-by-Step Breakdown

Let \( F_b \) be the buoyant force:

\[ F_b = \rho_{fluid} \cdot g \cdot V_{displaced} \]
  • Where \( \rho_{fluid} \) = density of fluid (kg/m³)
  • g = acceleration due to gravity (m/s²)
  • \( V_{displaced} \) = volume of fluid displaced (m³)

This upward force explains why objects float or sink based on their density relative to the fluid.

🔍 Option Analysis

  • A: a downward force - Incorrect; buoyancy opposes gravity.
  • B: a downward pressure - Incorrect; pressure in fluids acts in all directions, buoyancy is a force.
  • C: an upward force - Correct; it acts opposite to gravity.
  • D: an upward pressure - Incorrect; pressure contributes to buoyancy but is not the force itself.

⚡ Mnemonic / Speed-Run

Remember the phrase: “Buoyancy Beats Gravity” to recall that buoyant force acts upward.

6. Visual Suggestion

6. Visual Suggestion

Illustrate a diagram of an object submerged in water, highlighting the upward buoyant force arrows and the displaced water volume beneath it.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class IX Science, Chapter 9 (Gravitation)

Question 2 of 3 NDA MCQ

When a solid body is partially or completely immersed in a fluid, the fluid exerts an upward force on the body. The magnitude of the forceis equal to

1. The mass of the body

2. The weight of the displaced fluid by the body

Which of the above is/are correct?

Detailed Explanation
✓

1. Correct Answer

Option B is correct. The magnitude of the force is equal to the weight of the displaced fluid by the body.

📖 Core Concept

The question revolves around Archimedes' Principle, which explains the behavior of objects submerged in fluids.

💡 3. Explanation

Archimedes' Principle states:
Buoyant Force = Weight of Displaced Fluid
When a solid body is immersed in a fluid, the volume of fluid displaced is equal to the volume of the immersed part of the body. The mass of this displaced fluid, when multiplied by the acceleration due to gravity (g), gives us the buoyant force acting upwards against gravity.

The buoyant force F can be calculated by:
\[ F = \rho \times V \times g \]
Where:
  • \(\rho\) = density of the fluid
  • V = volume of the displaced fluid
  • g = acceleration due to gravity

❌ 4. Option Analysis

  • •Option A: The buoyant force is not equal to the mass of the body; it depends on the volume of the displaced fluid and not on the mass of the object.
  • •Option C: Although both the weight and volume of the body can influence displacement, buoyant force correlates specifically to fluid displacement.
  • •Option D: Neither statement is accurate; Archimedes' Principle specifically refers to the displacement of fluid weight, not the mass of the body or otherwise.
⚡

NDA Speed-Run / Mnemonic Shortcut

Remember: "Buoyant Force = Weight of Displaced Fluid" to quickly identify the answer in related questions.

🎯

5. Key Takeaways

The upward buoyant force equals the weight of the displaced fluid, as defined by Archimedes' Principle.

6. Visual Suggestion

Illustrate Archimedes’ Principle using a diagram showing a solid object immersed in fluid, emphasizing the volume of water displaced and the direction of the buoyant force.

Question 3 of 3 NDA MCQ

Buoyancy is a/an

Detailed Explanation

Correct Answer

✓ Option (d) is correct. Buoyancy is an upward force exerted by a fluid.

📖 Governing Law / Core Concept

Buoyancy is governed by Archimedes' Principle, which states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

🧪 Step-by-Step Breakdown

When an object is placed in a fluid, the pressure difference between the top and bottom surfaces of the object results in an upward force. This can be mathematically expressed as:

\[ F_b = \rho \cdot g \cdot V \]
Where:
  • \( F_b \) = Buoyant force (N)
  • \( \rho \) = Density of the fluid (kg/m³)
  • \( g \) = Acceleration due to gravity (9.81 m/s²)
  • \( V \) = Volume of fluid displaced (m³)

In this scenario, the fluid exerts more pressure at the bottom of the object than at the top, resulting in a net upward force responsible for buoyancy.

🔍 Option Analysis

Option A (upward pressure) incorrectly describes buoyancy as pressure rather than force. Option B (downward pressure) refers to atmospheric pressure and not relevant to buoyancy. Option C (downward force) contradicts the principle of buoyancy exerted by a fluid.

⚡ Mnemonic / Speed-Run

Remember the phrase “Archimedes’ Upward Push” to link buoyancy with its characteristic upward force.

6. Visual Suggestion

6. Visual Suggestion

A schematic diagram illustrating an object submerged in water, with arrows indicating fluid pressure at the bottom and top surfaces, highlighting the resultant upward buoyant force.

📖 Factual Verification & Reference

📖 Factual Verification & Reference:

Verified against NCERT Class IX Science, Chapter on Force and Pressure.

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