100k Followers100k500k Followers500k+1 (510) 706-9331+1 (510) 706-9331
Schedule Your Free Exam Readiness Analysis Session!
Testprepkart Logo
Sign InEnroll NowEnroll
Select an exam to view its content.
  • Blog
  • Download
  • Course
  • Result
  • Video Library
  • Pages
  • Notifications

Loading...

Preparing content

Testprepkart Logo

Enabling students prepare and crack toughest examinations worldwide for over a decade with problem solving aptitude!

Contact Us

Useful Links

  • Connect With Counselor
  • University Admissions
  • Prime Videos
  • Enrollment Form
  • Online Fee Payment
  • Testprepkart Operations
  • Faculty Registration

Our Company

  • Contact Us
  • Work With Us
  • Blogs
  • Facultie
  • Partner

Contact Details

  • Phone: +91 0120 4525484
  • Whatsapp: +1 (510) 706-9331
  • Admission: +91 8800123492
  • E-mail: info@testprepkart.com
  • Head Office: F 377, Sector 63, Noida, Uttar Pradesh, India

Copyright © 2024 CounselKart Educational Services Pvt. Ltd.. All Rights Reserved

Terms of service|Privacy policy|Refund Policy|Login & Register

Physical Quantity

NEET > Physics > Physical World and Measurement > Units, Dimensions and Measurement > Physical Quantity

Unit Progress

0%

Overview content

NEET Physics — Units, Dimensions and Measurement

Physical Quantity – Complete Notes, Revision, Important Questions & Downloads

Physical Quantity forms the conceptual gateway to the entire chapter on Units, Dimensions and Measurement. The topic centres on one subtopic — Definition and Representation — which establishes that every measurable quantity Q is expressed as Q = n × u, where n is the numerical value and u is the unit. NEET tests this relationship through unit-conversion numericals and assertion–reason items that probe the inverse proportionality n₁u₁ = n₂u₂. For instance, converting 1 joule into CGS units requires applying n₁u₁ = n₂u₂ with correct dimensional substitution, a pattern that appeared in NEET 2019 and 2021.

⬇ Download Notes PDFView Important Questions →
6 SubtopicsFoundational ConceptUnit Conversion Base
Expected QuestionsQ
0–1
Direct questions on the definition of physical quantity are rare; however, the Q = n × u framework underpins every unit-conversion and dimensional-analysis numerical in NEET.
Time Required⏱
1–2 hours
A short focused session to learn definitions and the n₁u₁ = n₂u₂ relation, plus practice with 5–10 conversion numericals.
Difficulty⚡
Easy
Conceptually straightforward; the challenge lies in applying the inverse relationship correctly during unit conversion with large exponent differences.
NRI USA Curriculum GapUS
Low
US high school physics (AP Physics 1) covers measurement and units at a comparable level, though the formal notation Q = n × u and the inverse-proportionality principle are rarely stated explicitly in American textbooks.
6Subtopics
8+Practice Questions
4Free Downloads
1–2 hrsPrep Time
⬇ Get Free Downloads

NEET Weightage — Physical Quantity

Units, Dimensions and Measurement (Chapter 1)
NEET YearQuestions from this TopicBarMarks
20240
 
0 Q
0
20231
 
1 Q
4
20220
 
0 Q
0
20211
 
1 Q
4
20200
 
0 Q
0
20191
 
1 Q
4
6-Year Total (2019–2024)1–3 4–12
The relation Q = n × u and n₁u₁ = n₂u₂ is the basis for every unit-conversion numerical in NEET — if n increases, u must decrease proportionally.
NEET occasionally frames assertion–reason questions asking whether happiness or beauty is a physical quantity; the answer depends on measurability, which is the textbook's opening criterion.

Physical quantity definition questions test whether the student can distinguish between a measurable quantity (e.g. force, energy) and a non-measurable experience (e.g. sorrow, taste).
📊
~0.3
Avg Questions / Year
🎯
4–12
Total Marks (6 yrs)
📈
Direct
Pattern
⚡
Easy
Difficulty

Exam Strategy for Physical Quantity in NEET Physics

1

Memorise the formal definition and the Q = n × u equation Commit the textbook definition: a physical quantity is one that can be measured and by which physical happenings can be expressed as laws. The product n × u = constant means that when you switch from SI to CGS, n changes inversely with u. The trap: forgetting to adjust the numerical value when the unit changes, leading to answers off by powers of 10.

2

Apply n₁u₁ = n₂u₂ to unit-conversion problems For any conversion, write n₁ and u₁ in the original system, then express u₁ in terms of u₂ using dimensional factors. For example, 1 N = 1 kg·m/s² = 1000 g × 100 cm / s² = 10⁵ dyne. The trap: applying the inverse relationship backwards — if the unit becomes smaller, the numerical value must become larger, not smaller.

3

Distinguish physical quantities from non-physical experiences NEET assertion–reason items may list comfort, anger, beauty alongside force, mass, and velocity. The test: can it be assigned a numerical magnitude and a unit? If not, it is not a physical quantity. The trap: assuming all commonly discussed attributes are physical quantities simply because they can be rated on a subjective scale.

Download Study Notes — Physical Quantity

PDF · Cheat Sheet · MCQ Set · PYQ
📘
Physical Quantity — Full Notes
Complete notes covering the definition of physical quantity, the Q = n × u representation, the inverse relation n₁u₁ = n₂u₂, and worked unit-conversion examples across SI and CGS systems.
6 subtopicsWorked examplesUnit conversion context
Download PDF
📗
Physical Quantity — Formula Sheet
One-page formula reference: Q = n × u, n₁u₁ = n₂u₂, n ∝ 1/u — key formulas, conditions, and one worked example per subtopic.
1 pageAll key formulas
Download PDF
📙
Physical Quantity — MCQ Practice
10 NEET-style MCQs testing the definition, measurability criterion, and n₁u₁ = n₂u₂ conversions across SI, CGS, and MKS systems.
10 MCQsDetailed solutions
Download PDF
📕
Physical Quantity — NEET-Style PYQ Practice
Collection of NEET-style practice questions on physical quantity identification, unit conversion using n₁u₁ = n₂u₂, and assertion–reason items on the measurability criterion.
NEET-styleAnswer key included
Download PDF

Subtopics in Physical Quantity

2-Column Table
Column AColumn B
Definition and Representation↗
Ratio (numerical value only)↗
Scalar (magnitude only)↗
Vector (magnitude and direction)↗
Fundamental quantities↗
Derived quantities↗

Rapid Revision — Physical Quantity

Concept → Trap → Example

1) Definition and Representation

Core Definition + Formula

Physical quantity (Q) = Magnitude × Unit = n × u. Since n × u = constant, n₁u₁ = n₂u₂, meaning n ∝ 1/u.

  • A physical quantity must be measurable and expressible in terms of laws — quantities like happiness, sorrow, and beauty fail this criterion and are not physical quantities.
  • The inverse proportionality n ∝ 1/u means that when you switch to a smaller unit, the numerical value increases proportionally: 1 kg = 1000 g, so n goes from 1 to 1000 while u shrinks from kg to g.
  • Common NEET trap: confusing the numerical value n with the physical quantity Q itself — n changes with unit choice, but Q (the actual measurable property) remains invariant.
Example (NEET-style)Convert 36 km/h to m/s using n₁u₁ = n₂u₂: n₁ = 36, u₁ = km/h = (1000 m)/(3600 s) = (5/18) m/s. So n₂ = 36 × (5/18) = 10 m/s. The product 36 × (km/h) = 10 × (m/s) confirms nu = constant.

US Curriculum Gaps — Physical Quantity

NRI students from US high schools may find these specific gaps when preparing for NEET Physics.

Formal Q = n × u representation (not covered in AP Physics 1)

US AP Physics 1 introduces measurement and units operationally but does not formalise the relationship Q = n × u or state the inverse proportionality n₁u₁ = n₂u₂ as a standalone principle. NEET expects students to apply this relation directly in conversion problems.

  • AP Physics 1 uses dimensional analysis for unit checks but not the explicit n₁u₁ = n₂u₂ formula.
  • NEET may ask: if the unit of force is doubled, by what factor does the numerical value change? The answer (halved) follows directly from n ∝ 1/u.
  • Practice rewriting Q = n × u and solving for n₂ given a new unit u₂.

Classification of non-physical quantities (not emphasised in US Honors Physics)

US Honors Physics and AP Physics courses assume students understand what a physical quantity is and do not test the distinction between measurable (physical) and non-measurable (non-physical) quantities. NEET assertion–reason questions sometimes test this boundary directly.

  • US courses rarely frame MCQs asking whether 'beauty' or 'comfort' is a physical quantity.
  • NEET expects a clear criterion: a physical quantity must be measurable and representable as n × u.
  • Practice identifying which everyday attributes lack units and therefore fail the measurability test.

NEET-Style Practice Questions — Physical Quantity

4 NEET-style practice questions
1The numerical value of a physical quantity is n₁ in SI units and n₂ in CGS units. If the ratio of the SI unit to the CGS unit for this quantity is 10³, then n₁/n₂ is:NEET-style practice
10³
10⁻³
1
10⁶
From n₁u₁ = n₂u₂, we get n₁/n₂ = u₂/u₁. If u₁ (SI unit) = 10³ × u₂ (CGS unit), then n₁/n₂ = u₂/u₁ = 1/10³ = 10⁻³. Option (a) reverses the ratio — it gives u₁/u₂ instead of u₂/u₁. Option (c) would hold only if the SI and CGS units were identical. Option (d) squares the ratio without justification. The key principle: n ∝ 1/u, so a larger unit gives a smaller numerical value.
2Which of the following is NOT a physical quantity?NEET-style practice
Strain
Refractive index
Anger
Relative density
A physical quantity must be measurable and expressible as a numerical value multiplied by a unit (Q = n × u). Strain, refractive index, and relative density are all measurable ratios of similar physical quantities — even though they are dimensionless, they qualify as physical quantities because they arise from measurement. Anger is a subjective emotional experience and cannot be assigned a reproducible numerical magnitude with a standard unit. Options (a), (b), and (d) are all valid dimensionless physical quantities. The measurability criterion from the textbook definition is the deciding test.
3If the fundamental unit of length is doubled, the numerical value of area will become:NEET-style practice
Doubled
Halved
Four times
One-fourth
Area has dimensions [L²]. Let the original unit of length be u and the numerical value of area be n. When the unit of length doubles (u' = 2u), the unit of area becomes (2u)² = 4u². By n₁u₁ = n₂u₂: n × u² = n' × 4u², so n' = n/4. The numerical value becomes one-fourth. Option (a) confuses length with area. Option (b) applies the length ratio linearly instead of squaring. Option (c) inverts the relationship — if the unit is larger, the numerical value decreases, not increases.
4A force of 100 N is expressed in a system where the unit of mass is 10 kg, unit of length is 1 km, and unit of time is 1 minute. The numerical value of the force in this new system is:NEET-style practice
36
3.6
360
0.36
Force has dimensions [MLT⁻²]. In SI: 100 N = 100 kg·m·s⁻². In the new system: M' = 10 kg, L' = 1 km = 1000 m, T' = 1 min = 60 s. Using n₁u₁ = n₂u₂ with dimensional factors: n₂ = n₁ × (M/M')¹ × (L/L')¹ × (T/T')⁻² = 100 × (1/10) × (1/1000) × (60/1)² = 100 × 0.1 × 0.001 × 3600 = 36. Option (b) misses one power of the time ratio. Option (c) incorrectly uses T'/T instead of T/T' for the ⁻2 exponent. Option (d) squares the mass ratio unnecessarily.

Practice Problems — Physical Quantity

Click "Reveal Answer" after attempting
1Express 1 joule in CGS units using the relation n₁u₁ = n₂u₂. Given: 1 J = 1 kg·m²·s⁻².
10⁷ erg
10⁵ erg
10³ erg
10⁹ erg
👁 Reveal Answer
Option (a): 10⁷ erg. Energy has dimensions [ML²T⁻²]. n₂ = n₁ × (M₁/M₂)¹ × (L₁/L₂)² × (T₁/T₂)⁻² = 1 × (1 kg / 1 g) × (1 m / 1 cm)² × (1 s / 1 s)⁻² = 1 × 10³ × (10²)² × 1 = 10³ × 10⁴ = 10⁷. Thus 1 J = 10⁷ erg.
2The density of mercury is 13600 kg/m³. Express this in g/cm³ using the relation n₁u₁ = n₂u₂.
13.6 g/cm³
1.36 g/cm³
136 g/cm³
1360 g/cm³
👁 Reveal Answer
Option (a): 13.6 g/cm³. Density has dimensions [ML⁻³]. n₂ = n₁ × (M₁/M₂)¹ × (L₁/L₂)⁻³ = 13600 × (1 kg / 1 g) × (1 m / 1 cm)⁻³ = 13600 × 10³ × (10²)⁻³ = 13600 × 10³ × 10⁻⁶ = 13600 × 10⁻³ = 13.6. Thus 13600 kg/m³ = 13.6 g/cm³.
3If the unit of force is 1 kN and the unit of length is 1 km, what is the unit of energy in this system expressed in SI joules?
10⁶ J
10³ J
10⁹ J
10¹² J
👁 Reveal Answer
Option (a): 10⁶ J. Energy = Force × Distance. In this system, 1 unit of energy = 1 kN × 1 km = 10³ N × 10³ m = 10⁶ N·m = 10⁶ J. The key is recognising that energy has dimensions [ML²T⁻²] = [Force × Length], so the new unit equals the product of the redefined force and length units.
4The speed of light is 3 × 10⁸ m/s. In a system where the unit of length is 1 km and the unit of time is 1 microsecond (μs), the numerical value of the speed of light is:
0.3
3 × 10²
3 × 10¹⁴
3 × 10⁵
👁 Reveal Answer
Option (a): 0.3. Speed has dimensions [LT⁻¹]. n₂ = n₁ × (L₁/L₂) × (T₁/T₂)⁻¹ = 3 × 10⁸ × (1 m / 1000 m) × (1 s / 10⁻⁶ s)⁻¹ = 3 × 10⁸ × 10⁻³ × 10⁻⁶ = 3 × 10⁻¹ = 0.3. The numerical value drops dramatically because the new length unit is large (km) and the new time unit is tiny (μs), making the speed unit itself very large.

Physics — Physical Quantity Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Tip: Mark a chapter complete only after revising formulas, solving PYQs, and reviewing your error log for that chapter.

Frequently Asked Questions — Physical Quantity

Notes · Downloads · Revision · Important Questions
What is a physical quantity according to NCERT?
A physical quantity is any quantity that can be measured and by which various physical happenings can be explained and expressed in the form of laws. The textbook gives length, mass, time, and force as examples. The key criterion is measurability — a quantity must have a reproducible numerical magnitude and a defined unit to qualify.
What does Q = n × u mean and why is it important for NEET?
Q = n × u states that every physical quantity Q equals its numerical value n multiplied by its unit u. This is important because NEET unit-conversion numericals require you to use the corollary n₁u₁ = n₂u₂: when you change the unit, the numerical value adjusts inversely. For example, 1 newton in CGS becomes 10⁵ dyne because the CGS unit of force (dyne) is 10⁻⁵ times the SI unit (newton).
Are dimensionless ratios like strain and refractive index considered physical quantities?
Yes. Strain, refractive index, and relative density are all physical quantities even though they have no unit. They are ratios of two similar physical quantities and are obtained through measurement. A physical quantity does not necessarily require a unit with dimensions — it requires measurability. NEET has tested this distinction in assertion–reason format.
What is the inverse relationship between numerical value and unit?
From Q = n × u = constant, we get n ∝ 1/u. This means: if you use a larger unit, the numerical value decreases, and vice versa. For instance, 1 km = 1000 m — the unit km is 1000 times larger than m, so the numerical value drops from 1000 to 1 when switching from metres to kilometres for the same distance.
How do I convert a physical quantity from one system of units to another?
Use the formula n₂ = n₁ × (M₁/M₂)^a × (L₁/L₂)^b × (T₁/T₂)^c, where [M^a L^b T^c] are the dimensions of the quantity. Find a, b, c from the dimensional formula. Substitute the ratio of the fundamental units. For example, to convert 1 J (SI) to CGS: [Energy] = [ML²T⁻²], so n₂ = 1 × (10³)^1 × (10²)^2 × (1)^(-2) = 10⁷. Hence 1 J = 10⁷ erg.
Is happiness a physical quantity?
No. The textbook explicitly states that happenings like happiness, sorrow, and similar experiences are not physical quantities because they cannot be measured with a numerical magnitude and a reproducible unit. The measurability criterion is the fundamental dividing line. This distinction is sometimes tested in NEET as an assertion–reason question.
What is the difference between magnitude and numerical value?
The magnitude of a physical quantity includes both the numerical value and the unit: for example, the magnitude of a length is 5.2 m. The numerical value alone is 5.2. When you say n × u, n is the numerical value and u is the unit; the product n × u gives the complete magnitude. A negative numerical value (e.g. −5 °C) indicates the direction on a scale, not a spatial direction.
Can a physical quantity have a negative numerical value?
Yes. A negative numerical value simply means the quantity is below a chosen reference point on its measurement scale. Temperature can be −10 °C; work done by friction is negative. The negative sign does not imply direction in the vector sense — it indicates that the numerical value is less than zero, which is a valid outcome of measurement. The textbook clarifies this under scalar quantities.
For NRI / OCI / U.S.-Based Families

NEET NRI Counseling & Admission eBook Download

A practical guide covering sponsor rules, document checklist, verification traps, NRI quota reality, and step-by-step counselling flow. Designed to prevent last-minute rejections and wrong choice filling.

Sponsor + Proof ClarityDocuments ChecklistState-wise Traps
↓ Download eBook (PDF)→ See What's Inside
Tip: Keep this eBook open during verification + choice filling week for quick cross-checking.
NEET Prep (India + NRI-USA)

Schedule Trial Session For NEET Prep

Get a short diagnostic + study roadmap: syllabus gaps (NCERT vs U.S. curriculum), weak chapters, and the exact weekly plan needed to improve accuracy under time.

Gap MappingWeekly PlanAccuracy Fix
→ Book Trial Session→ WhatsApp Us
Best for: Students in Grade 10–12 (U.S. / India) who want a clear NEET timeline and daily practice structure.

Definition and Representation

Ratio (numerical value only)

Scalar (magnitude only)

Vector (magnitude and direction)

Fundamental quantities

Derived quantities

Subtopics

Definition and Representation

Ratio (numerical value only)

Scalar (magnitude only)

Vector (magnitude and direction)

Fundamental quantities

Derived quantities

Previous
Physical Quantity > Derived quantities > Derived quantities
Next
Definition and Representation

Loading tests...

NEET > Physics > Physical World and Measurement Chapters

Review your status and progress for each chapter in this unit. Use the slider to set progress or click "Mark as Done" to complete.

ChapterStatusProgress

Fundamental Mathematics and Vector

Weightage: 02.2K
0%

Units, Dimensions and Measurement

Weightage: 02.2K
0%

Comments

Leave a comment

0/2000Comments are moderated

You can comment without logging in. We'll ask for your name and email before submitting.

Comments (0)

No comments yet. Be the first to comment!