Dimensional Analysis Questions

Dimensional Analysis is also known as the factor-label method or the unit factor method. Dimensional analysis helps to understand the relationships between various physical quantities by recognising their base quantities as well as units. In the year 1822, Joseph Fourier introduced the concept of dimensional analysis.

Dimension refers to the physical nature of a quantity and the type of unit used to specify it. Dimensional analysis is known as the factor label method or unit factor method since conversion factors are used to obtain the same units.

Some applications of dimensional analysis are:

  • It is used to inspect the consistency of a dimensional equation
  • To change units from one system to another
  • To get the relation between physical quantities in physical phenomena

Limitations of dimensional analysis are:

  • The dimensional analysis does not give information about the dimensional constant.
  • The formula which features logarithmic functions, trigonometric functions, and exponential functions, cannot be derived using dimensional analysis.
  • The dimensional analysis offers no information on whether a physical quantity is a scalar or vector.

Constants that have dimensions are known as dimensional constants.

Example: Planck’s constant, gravitational constant

Physical quantities which possess dimensions but do not have a fixed value are called dimensional variables. Examples: velocity, displacement, and force.

Angle, specific gravity, strain are some of the dimensionless quantities. Physical quantities with no dimensions are known as dimensionless quantities.

Some of the basic dimensions are Length – L, Time – T, Mass – M, Temperature – K or θ, and Current – A.

List of physical quantities having the same dimensional formula are:

impulse and momentum

power, luminous flux

angular velocity, frequency, velocity gradient

work, energy, torque, the moment of force, energy

thermal capacity, entropy, universal gas constant and Boltzmann’s constant

force constant, surface tension, surface energy.

angular momentum, Planck’s constant, rotational impulse

latent heat, gravitational potential.

force, thrust

stress, pressure, modulus of elasticity

Important Dimensional Analysis Questions with Answers

1. Dimension formula of luminous flux matches with which of the following?

  1. Force
  2. Rotational impulse
  3. Momentum
  4. Power

Answer: d) Power

Explanation: Dimensional formula of power is M^{1}L^{2}T^{-3}, and Dimensional formula of luminous flux is also M^{1}L^{2}T^{-3}.

2. Who introduced the concept of dimensional analysis?

The concept of dimensional analysis was introduced by Joseph Fourier in the year 1822.

3. What is dimensional analysis, is also known as _____?

Dimensional Analysis is also known as the factor-label method or the unit factor method.

4. Which among the following is not a basic unit of measurement?

  1. Time
  2. Temperature
  3. Momentum
  4. Mass

Answer: c) Momentum

Explanation: Momentum is not a basic unit of measurement. It is a derived unit.

5. State true or false: dimensional analysis helps to know if the physical quantity is a vector or a scalar quantity.

  1. TRUE
  2. FALSE

Answer: b) FALSE

Explanation: Dimensional analysis offers no information on whether a physical quantity is a scalar or vector.

6. Match with the same dimensional formula quantity.

  1. Force    a) Latent heat
  2. Rotational impulse    b) luminous flux
  3. Gravitational potential     c) Thrust
  4. Power     d) Planck’s constant
  1. 1-c), 2-d), 3-a) , 4-b)
  2. 1-d), 2-c), 3-a) , 4-b)
  3. 1-a), 2-b), 3-c) , 4-d)
  4. 1-d), 2-c), 3-b) , 4-a)

Answer: 1-c), 2-d), 3-a) , 4-b)

7. Identify the dimensional constant.

  1. Force
  2. Momentum
  3. Planck’s constant
  4. Specific gravity

Answer: c) Planck’s constant

8. Mention two-dimensional variables.

Two-dimensional variables are Force and Velocity.

9. Identify the dimensionless quantity.

  1. Angle
  2. Specific gravity
  3. Strain
  4. All the above options

Answer: d) All the above options.

10. Define dimensionless quantities.

Physical quantities which do not possess dimensions are known as dimensionless quantities.

Practice Questions

  1. Define dimensional analysis.
  2. Mention three pairs that have the same dimensional formula.
  3. What are dimensional variables?
  4. What is the dimensional formula for entropy?
  5. List the applications of dimensional analysis.

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