Dimensions and Dimensional Analysis

These flashcards cover essential concepts and definitions related to dimensions and dimensional analysis in physics, preparing students for exams.

What are dimensions in physics?

Powers to which fundamental quantities are raised to represent a physical quantity.

What are the fundamental quantities in mechanics?

Mass (M), Length (L), and Time (T).

How is force defined in terms of mass and acceleration?

Force = mass x acceleration.

What are the dimensions of force?

[M1L1T-2] (1 in mass, 1 in length, -2 in time).

Define dimensionless quantity.

A physical quantity with no physical units, like strain or angle.

Can a dimensionless quantity have a unit?

Yes, it may have a unit but cannot be expressed in fundamental SI quantities.

What is the dimensional formula for density?

[M1L-3T0] (mass per volume).

What is the dimensional formula for power?

[M1L2T-3] (work per time).

How do you calculate the dimensions of the coefficient of viscosity?

[M1L-1T-1] based on mass, acceleration, distance, and time.

What does dimensional analysis help to establish?

Establish the form of an equation and check calculations for errors.

What is the principle of homogeneity of dimensions?

Dimensions of all terms in an equation must be the same.

Why is the principle of homogeneity useful?

It helps to check the correctness of physical equations.

What is the dimensional representation of length (S)?

[L1].

What is the dimensional representation of velocity (u)?

[L1T-1].

What is the relationship between work and energy?

They have the same dimensions of [M1L2T-2].

How is work dimensionally defined in relation to force?

Work = force x distance = [M1L2T-2].

How do you check the correctness of a physical equation?

Ensure all terms have the same dimensions.

What dimensions do constants have in an equation?

Constants are dimensionless.

Define a dimensionally homogeneous equation.

An equation where all terms have the same dimensions.

What is the dimensional formula for gravitational force?

[M1L1T-2].

What is the context for the expression F = ax + bt²?

In this expression, F is force, x is distance, and t is time.

What dimensions does 'a' have in the equation F = ax + bt²?

[MLT-2].

What dimensions does 'b' have in the expression F = ax + bt²?

[ML-1T-2].

What limitations does dimensional analysis have?

It doesn’t determine dimensional constants or work with trigonometric functions.

How is the universal gas constant dimensionally represented?

[M1L2T-2K-1].

How do you derive the dimensions of pressure?

Pressure = Force/Area = [M1L-1T-2].

What are the dimensions of specific heat capacity?

[M0L2T-2K-1].

How do you find dimensions for a derived quantity?

Set up the equation and equate the powers of fundamental dimensions.

What is the significance of the dimensions in electromagnetic force?

EMF is represented as [M1L2T-3I-1].

What role does dimensional analysis play in physics?

It aids in validating equations and converting units.

What must be true about the dimensions in equations involving pressure and volume?

They must maintain dimensional homogeneity.

When deriving the time period of a pendulum, what dimensions are needed?

Combine mass (M), length (L), and gravity (g) accordingly.