UNITS & DIMENSIONS---What are Physical Quantities?

 

Introduction: Why Physical Quantities Matter?

Imagine you're an engineer designing a rocket or a doctor calculating the dosage of a life-saving drug. How do you ensure precision? The answer lies in physical quantities—the measurable properties that define the universe. For NEET, JEE Mains, and JEE Advanced aspirants, mastering these is crucial because every equation, every experiment, and every discovery in physics relies on them!

A physical quantity is any measurable property of a physical system, expressed as a numerical value and a unit. All the quantities which are used to describe the laws of physics are known as physical quantities.

Example:

• Mass of an electron = 9.11 × 10⁻³¹ kg
• Speed of light = 3 × 10⁸ m/s

Key Features:

1. Measurable (can be quantified using instruments).
2. Has a unit (like meters, seconds, kilograms).
3. Can be scalar (magnitude only) or vector (magnitude + direction).

In physics, Physical Quantities are those properties of a material or a system that can be measured using instruments and are expressed with a numerical value and a unit.

In simple words, anything you can measure — like time, length, mass, temperature, speed, force — is a physical quantity.

Why are Physical Quantities Important?

• They form the backbone of all scientific laws and theories.
• Every equation in physics (e.g. Newton's laws, equations of motion, thermodynamics) is written in terms of physical quantities.
• Understanding physical quantities helps students quantify natural phenomena — making abstract ideas concrete and calculable.

Classification: Physical quantities can be classified on the following basis:

Physical quantities are divided into two broad categories:

(I)Based on their dependency:

1.Fundamental Quantities (Base Quantities)

These are the basic quantities which cannot be broken down further. These are independent and form the foundation for other quantities. The quantities which do not depend upon other quantities for their complete definition are known as fundamental or base quantities There are 7 fundamental quantities in the SI system:

Fundamental Quantity	SI Unit	Symbol
Length	Meter (m)	L
Mass	Kilogram (kg)	M
Time	Second (s)	T
Electric Current	Ampere (A)	I
Temperature	Kelvin (K)	θ
Amount of Substance	Mole (mol)	N
Luminous Intensity	Candela (cd)	J

 

Case Study: The Kilogram Redefinition (2019)

Earlier, the kilogram was defined by a physical platinum-iridium cylinder in France. But in 2019, it was redefined using Planck’s constant (h) for extreme precision. This shows how fundamental units evolve with science!

JEE/NEET Note: You must memorize these 7 base quantities and their SI units. They are often asked in assertion-reasoning and unit conversion problems.

2.Derived Quantities

These are quantities derived from the fundamental ones using mathematical relations. These are combinations of fundamental quantities. The quantities which can be expressed in terms of the fundamental quantities are known as derived quantities.

Examples:

·        Force (F) = mass × acceleration → [M L T⁻²] → Newton (N)

·        Energy (E) = Force × distance → [M L² T⁻²] → Joule (J)

Derived Quantity	Expression	SI Unit	Example
Velocity	Distance/Time	m/s	Speed of a car
Acceleration	Velocity/Time	m/s²	Free-fall
Force	Mass × Acceleration	N (newton)	Pushing a door
Pressure	Force/Area	Pa (pascal)	Air pressure
Energy	Work done	J (joule)	Heat energy, mechanical work

(II) Based on their directional properties:

1.Scallars: The physical quantities which have only magnitude but no direction is called scalar quantities.

Examples: Mass, Density, Volume, time, etc.

2.Vectors: The physical quantities which have both magnitude and direction and obey laws of vector algebra are called vector quantities.

Examples: Displacement, Force, Velocity, etc.

Scalar (Magnitude Only)	Vector (Magnitude + Direction)
Mass, Time, Speed	Velocity, Force, Acceleration
Example: Temperature (30°C)	Example: Displacement (5 m East)

NEET/JEE Application:

• Scalars follow ordinary algebra.
• Vectors need vector algebra (dot & cross products).

Physical quantities can also be classified as dimensional and dimensionless quantities or constants and variables.

JEE Advanced Concept: Dimensional Analysis

If Pressure (P) = Force/Area, its dimensional formula is [M L⁻¹ T⁻²]. This helps verify equations and derive relationships!

Examples: Classify the quantities displacement, mass, force, time, speed, velocity, acceleration, moment of inertia, pressure and work under the following categories:

(a)Base and scalar (b) base and vector (c) derived and scalar (d) derived and vector

Solution:

(a)   Mass, time (b) displacement (c) speed, pressure, work (d) force, velocity, acceleration

Case Study 1: Free-Fall from a Building (NEET & JEE Scenario)

Let’s say a medical student is watching a ball drop from a building. A JEE aspirant calculates the acceleration due to gravity.

• Fundamental quantities involved:
• Mass of ball (kg)
• Time taken to fall (s)
• Length of fall = Height (m)
• Derived quantity:
• Velocity and acceleration (m/s, m/s²)
• Using the equation:
  s=ut+1/2at²

This real-life observation uses at least 4 physical quantities!

Case Study 2: Measuring Temperature in a Chemical Reaction (NEET Biology + Physics Crossover)

A NEET student is monitoring a reaction in a lab.

• The rise in temperature (K) is measured.
• The mass of the reactants (kg) and time (s) taken for completion are also recorded.
• Energy released is a derived quantity, calculated using:
  Q=mcΔT

Real-World Applications & Problem-Solving

Case Study 1: Rocket Launch (JEE Advanced)

A rocket’s thrust depends on:

• Force (F = ma) → Derived from mass (fundamental) and acceleration (derived).
• Velocity (v = u + at) → Combines time (fundamental) and acceleration.

Problem: If a rocket of mass 5000 kg accelerates at 20 m/s², what’s the thrust force?
Solution:

F=ma=5000×20=10⁵ N

Case Study 2: Medical Dosage (NEET)

A doctor prescribes a drug dosage based on mass (kg) and time (hours).

Problem: If a patient (60 kg) needs 3 mg/kg every 4 hours, what’s the single dose?
Solution:

Dose=60×3=180 mg

This example connects physics with chemistry and shows how physical quantities unify science disciplines.

Real-Life Application: Speed Radar Gun (JEE Advanced Type Concept)

When a traffic police officer measures the speed of a car using a radar gun:

• Radar uses Doppler effect (Advanced Physics)
• Quantities measured:
• Frequency (Hz), Time (s), Distance (m)
• Derived Quantity: Speed (m/s)

This shows how physics is applied practically using physical quantities.

Common MCQ Trick in Exams

Q: Which of the following is NOT a physical quantity?
a) Mass
b) Anger
c) Force
d) Time

Answer: b) Anger — because it cannot be measured.

Final Thoughts

Physical quantities are not just numbers — they are the language of physics. Without them, we couldn’t define, measure, or predict anything in science.

Einstein once said:
“If you can’t measure it, you don’t understand it.”

Mastering physical quantities will make you more confident in solving physics problems, writing neat derivations, and thinking like a scientist.

Pro Tips for NEET/JEE Aspirants

1. Memorize the 7 fundamental quantities.
2. Practice dimensional analysis to check equation validity.
3. Differentiate scalars & vectors for mechanics problems.
4. Always write physical quantities with their units.
5. Remember: You can't add or subtract quantities with different dimensions (e.g., can’t add speed and force).

Conclusion: Master Physical Quantities to Dominate Physics!

Whether it’s Newton’s laws, thermodynamics, or electromagnetism, every concept in physics boils down to physical quantities. By understanding them deeply, you’ll solve complex problems faster and ace competitive exams!

Challenge Yourself:

• Derive the dimensional formula for Power.
• Is angular momentum scalar or vector?

Drop your answers below! Let’s see who gets it right!