Dimensional analysis – problems and solutions

1. Based on the dimensional analysis, determine the following physics dimensions that have the same dimensions.

B. power and pressure

C. force and momentum

D. work and heat

__Known :__

Dimension of length = dimension of width = dimension of displacement = L

Dimension of time = T

Dimension of mass = M

__Solution :__

Dimension of area = dimension of length x dimension of width = [L][L] = [L]^{2}

Dimension of velocity = dimension of displacement / dimension of time = [L] / [T] = [L][T]^{-1}

Dimension of acceleration = dimension of velocity / dimension of time = [L][T]^{-1 }/ [T] = [L][T]^{-1}[T]^{-1} = [L][T]^{-2}

Dimension of force = dimension of mass x dimension of acceleration = [M][L][T]^{-2}

Dimension of work = dimension of force x dimension of displacement = [M][L][T]^{-2 }[L] = [M][L]^{2}[T]^{-2}

Dimension of power = dimension of work / dimension of time = [M][L]^{2}[T]^{-2} / [T] = [M][L]^{2}[T]^{-2}[T]^{-1} = [M][L]^{2}[T]^{-3}

Dimension of pressure = dimension of force / dimension of area = [M][L][T]^{-2} / [L]^{2 }= [M][L][T]^{-2 }[L]^{-2 }= [M] [L]^{-1}[T]^{-2 }

Dimension of momentum = dimension of mass x dimension of velocity = [M][L][T]^{-1}

Dimension of heat = dimension of energy = dimension of work = [M][L]^{2}[T]^{-2}

The correct answer is D.

Note :

Heat is energy that moves due to the temperature difference.

Work is the process of energy transfer through the displacement of objects.

So, the dimension of heat = the dimension of energy = the dimension of work.

2. Two quantities that have the same quantity but have a different physical concept…

A. Force and momentum

B. Energy and force

C. Potential energy and kinetic energy

D. Energy and momentum

Solution :

Unit of potential energy = unit of kinetic energy = unit of energy = unit of work.

Although it has the same unit, but the potential energy and the kinetic energy are different types of energy.

The correct answer is C.

3. The following quantities that have the same units are…

A. Force and emf

B. Velocity and acceleration

C. Work and energy

D. Work and power

Solution :

Work is the process of energy transfer through the displacement of objects.

Energy is the ability to do work.

Work and energy are two quantities of physics that have the same unit.

The correct answer is C.