Blog Image

A Complete Guide to Units,Measurements & Dimensional Concepts for NEET,JEE & CUET Aspirants

Table of Contents

Introduction

Units and Measurements is one of the most conceptually rich chapters for NEET Physics, JEE Physics, and CUET Physics. It introduces fundamental ideas like physical quantities, dimensional formulae, dimensional analysis, base units, derived units, significant figures, and unit conversions. These ideas continue to appear in mechanics, electricity, magnetism, modern physics, fluid dynamics, thermodynamics, and optics.

Dimensional analysis enables students to verify equations, derive relations, convert quantities across systems, and evaluate the correctness of formulas. Understanding the units of physical constants—like permittivity, permeability, Planck’s constant, gravitational constant, electrical conductivity, surface tension, and thermal conductivity—is essential for scoring full marks in competitive exams.

This blog includes all major units and measurements keywords, such as dimensional analysis, dimensional formula, permittivity of free space, permeability, SI units, coefficient of viscosity, surface tension, conductivity, strain, Young’s modulus, electron mobility, dioptre, molar gas constant, parsec, light year, gravitational constant, and electric field units.

Understanding Units and Measurements

Physical Quantities

Physics is built around measurable quantities. They are categorized into:

  • Fundamental (Base) Quantities
    Mass, length, time, temperature, electric current, luminous intensity, amount of substance.

  • Derived Quantities
    Speed, acceleration, force, pressure, energy, power, surface tension, electrical resistance, electrical conductivity.

Dimensional Formula

The dimensional formula expresses a physical quantity in terms of M, L, and T (and A for current). For example:

  • Force → [MLT⁻²]

  • Pressure → [ML⁻¹T⁻²]

  • Energy → [ML²T⁻²]

  • Planck’s constant → [ML²T⁻¹]

  • Permeability μ₀ → [MLT⁻²A⁻²]

Dimensionless and Unitless Quantities

Some values are dimensionless but may have a unit (or vice versa). Examples include:

  • Dimensionless and unitless: refractive index, relative density

  • Dimensional but unit-based: angle (radian), solid angle (steradian)

  • Unitless but derived: strain, Poisson’s ratio

Systems of Units

Familiarity with systems like CGS, MKS, FPS, and the universal SI system is essential. SI units unify all measurements using coherent units like:

  • Newton (force)

  • Joule (energy)

  • Pascal (pressure)

  • Siemens (conductance)

  • Weber (magnetic flux)

  • Henry (inductance)

Advanced MCQs from Units, Measurements & Dimensional Analysis

1. Which is not the unit of electric field?

a) N/C
b) N·m/C
c) V/m
d) J/C·m

Answer: b

2. SI unit of coefficient of viscosity is

a) N s m⁻²
b) N s⁻¹ m²
c) N s m⁻³
d) N s⁻² m

Answer: a

3. Which of the following is the smallest unit?

a) Millimetre
b) Angstrom
c) Fermi
d) Metre

Answer: c

4. Which of the following quantities has a unit but is dimensionless?

a) Strain
b) Reynold’s number
c) Angular displacement
d) Poisson’s ratio

Answer: c

5. Young’s modulus has the same units as

a) Pressure
b) Strain
c) Compressibility
d) Force

Answer: a

6. The unit of inductance is equal to

a) Volt–sec/Amp
b) Volt × Amp/sec
c) Volt × sec/Volt
d) Volt/Amp × sec

Answer: a

7. SI unit of dipole moment is

a) C·m
b) C·m²
c) C/m²
d) C/m

Answer: a

8. In v = at² + bt + c, with v in m/s and t in s, the unit of b is

a) a is m/s
b) b is m⁻¹
c) c is m/s
d) a and d same but c different

Answer: c

9. Unit of surface tension in SI system is

a) N·m
b) N·m⁻¹
c) N·m²
d) N·m⁻²

Answer: b

10. Which pair may be represented in the same unit?

a) Heat and temperature
b) Temperature and mole
c) Heat and work
d) Specific heat and heat

Answer: c

11. Which physical quantity has no unit?

a) Luminous intensity
b) Momentum
c) Current
d) Refractive index

Answer: d

12. In v = A + Bt + Ct², if v is in m/s, the unit of A is

a) m/s
b) m/s²
c) ms
d) m²/s

Answer: a

13. In Bernoulli’s equation P + ½ρv² + hρg = K, the unit of K/P is

a) Pressure
b) Thrust
c) Angle
d) None

Answer: d

14. Unit of electrical conductivity is

a) ohm
b) siemen
c) m/mho
d) mho/m

Answer: d

15. SI unit of wave intensity is

a) J m⁻² s⁻1
b) J m⁻¹ s⁻2
c) W m⁻²
d) J m⁻²

Answer: c

16. The unit of permittivity of free space ε₀ is

a) C/(N·m)
b) N·m²/C²
c) C²/(N·m²)
d) C²/(N·m)²

Answer: c

17. If x = at + bt² with x in km and t in seconds, unit of b is

a) km/s
b) km·s
c) km/s²
d) km·s²

Answer: c

18. SI unit of moment of inertia is

a) kg m⁻²
b) kg m²
c) N m⁻²
d) N m²

Answer: b

19. Siemen is SI unit for

a) Electrical resistivity
b) Electrical conductance
c) Electrical permittivity
d) Electrical capacitance

Answer: b

20. The SI unit of mechanical equivalent of heat is

a) J/cal
b) J–cal
c) cal·erg
d) erg/J

Answer: a

21. ______ system was accepted by the conference on weights and measures.

a) FPS
b) CGS
c) MKS
d) SI

Answer: d

22. SI unit of gravitational constant is

a) N m kg
b) N m² kg⁻²
c) N m² kg
d) N⁻¹ m⁻² kg

Answer: b

23. Correct unit of thermal conductivity is

a) J m⁻² s⁻¹ (°C)⁻¹
b) J m⁻¹ s⁻¹ (°C)⁻²
c) J·s
d) J m⁻¹ s⁻¹ (°C)⁻¹

Answer: d

24. Unit of polarizability of molecule is

a) C² m N⁻1
b) C⁻2 m⁻1 N¹
c) C⁻2 m N⁻1
d) C² m⁻1 N⁻¹

Answer: a

25. Which is not a unit of surface tension?

a) N/m
b) J/m²
c) kg/s²
d) W/m

Answer: d

26. Dioptre is the unit of

a) Power of lens
b) Focal length
c) Ionosphere
d) None

Answer: a

27. In a system with units A kg, B m, C s, the value of 10 N is

a) 10 A⁻¹ B⁻¹ C⁻²
b) 10 A⁻¹ B⁻¹ C²
c) 10 A B C⁻²
d) 5 A⁻¹ B C²

Answer: b

28. The CGS unit of magnetic field (Biot–Savart law) is

a) Tesla
b) Gauss
c) Tesla·m/A
d) Newton/Amp

Answer: b

29. Which is both unitless and dimensionless?

a) Angle
b) Solid angle
c) Mechanical equivalent of heat
d) Refractive index

Answer: d

30. The unit of relative permittivity is

a) C² N⁻¹ m⁻2
b) N m² C⁻²
c) Unitless
d) N C⁻² m⁻2

Answer: c

Conclusion

Units and Measurements is a scoring chapter in NEET, JEE and CUET. Knowing the dimensional formulae of constants, the units of derived quantities, and the classification of dimensionless values gives students a major advantage. The MCQs included above cover all the most frequently asked concepts such as surface tension, coefficient of viscosity, inductance, permittivity, electric field, magnetic field, Young’s modulus, thermal conductivity, electrical conductivity, and more.

Leave A Comment