Dimensional Formula For Force Of Buoyancy

Dimensional Formula:

\[ [M L T^{-2}] \]

Dimensions:

M (mass, kg)

L (length, m)

T (time, s)

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1. What is the Dimensional Formula for Force of Buoyancy?

Definition: The dimensional formula [M L T⁻²] represents the fundamental physical dimensions that make up the force of buoyancy.

Purpose: It helps in understanding the relationship between buoyant force and its fundamental quantities in physics.

2. Understanding the Components

The formula consists of:

\[ [M L T^{-2}] \]

Where:

M — Mass (kilograms)
L — Length (meters)
T — Time (seconds)

Explanation: This matches the dimensional formula for force in general, as buoyant force is a type of force.

3. Importance in Physics

Details: The dimensional formula is crucial for:

Verifying equations involving buoyant force
Converting between unit systems
Understanding the fundamental nature of buoyancy
Deriving other related physical quantities

4. Relation to Buoyant Force Equation

The buoyant force (F) is calculated by:

\[ F = \rho V g \]

Where:

ρ — fluid density [M L⁻³]
V — displaced volume [L³]
g — acceleration due to gravity [L T⁻²]

Combining these gives the dimensional formula [M L T⁻²]

5. Frequently Asked Questions (FAQ)

Q1: Why is the dimensional formula important?
A: It helps verify the correctness of physical equations and enables unit conversions.

Q2: How does this relate to Archimedes' principle?
A: Archimedes' principle describes buoyant force, and this formula shows its fundamental dimensions.

Q3: Is this the same as weight's dimensional formula?
A: Yes, because both are forces, though they have different physical meanings.

Q4: Can this formula change in different unit systems?
A: No, the fundamental dimensions remain the same, though the units may differ.

Q5: How is this used in practical applications?
A: Engineers use dimensional analysis to design ships, submarines, and floating structures.