• Amal Augustine
• November 28, 2025

Units, Measurements & Errors Mastery: A Complete Guide for NEET, JEE and CUET Aspirants

Understanding units, dimensions, significant figures and error analysis is one of the earliest yet most important foundations in Class 11 Physics. For competitive exams like NEET, JEE and CUET, this chapter frequently appears in both theory and MCQ sections. Students often struggle with dimensional formulas, error propagation and identifying dimensionless quantities, so this guide brings everything together in one place.

Below is a structured explanation of key concepts followed by 30 exam-focused MCQs with answers, ensuring you get both conceptual clarity and practice. Keywords like dimensional analysis, significant figures, error percentage, unit conversion, precision, accuracy, vernier calipers, screw gauge least count, pressure error, density calculation and physical quantities are integrated naturally to help your preparation.

Understanding Dimensions and Units

Dimensional analysis helps verify equations, convert physical quantities and deduce relationships among variables. Students should remember the dimensional formulas of standard quantities like force, pressure, angular velocity, torque, stress and energy. This topic is also directly connected to error estimation and significant figures, where precision and accuracy become essential.

Important Concepts for Competitive Exams

Significant Figures

Significant figures represent the precision of a measured quantity. Rules for counting significant digits, rounding off values and calculating errors are crucial for Physics experiments and numerical problems.

Error Analysis

Percentage error, absolute error and the rules for error propagation in products, quotients and powers appear frequently in competitive questions.

Measuring Tools

Least count of vernier calipers, screw gauge and stop watch must be understood clearly to solve experiment-based numerical problems.

MCQs on Units, Dimensions, Errors and Measurement (With Answers)

1. A force is given by F = at + bt². The dimensions of a and b are:

A) [MLT⁻⁴] and [MLT⁻¹]
B) [MLT⁻¹] and [MLT⁰]
C) [MLT⁻³] and [MLT⁻⁴]
D) [MLT⁻³] and [MLT⁰]
Correct Answer: C

2. Mass of a body is 210 g and density is 7.981 g/cm³. Volume is:

A) 26.312 cm³
B) 26 cm³
C) 27 cm³
D) 26.3 cm³
Correct Answer: B

3. Significant figures in 23.023, 0.0003 and 2.1 × 10³ are:

A) 5, 1, 2
B) 5, 1, 5
C) 5, 4, 2
D) 5, 1, 5
Correct Answer: A

4. If error in L = 2% and in F = 4%, pressure error is:

A) 2%
B) 4%
C) 6%
D) 8%
Correct Answer: D

5. If X = MᵃLᵇTᶜ and M, L, T have errors a%, b%, c%, then % error in X:

A) (aα + bβ + γc)%
B) (aα − βb + γc)%
C) (αa − βb − γc)%
D) None of these
Correct Answer: A

6. Relative density using spring balance (5.00 ± 0.05) N in air and (4.00 ± 0.05) N in water:

A) (5.00 ± 0.05)
B) (5.00 ± 11%)
C) (5.00 ± 0.10)
D) (5.00 ± 6%)
Correct Answer: D

7. Least count of screw gauge (pitch = 0.5 mm, divisions = 50):

A) 0.001 mm
B) 0.01 mm
C) 0.02 mm
D) 0.025 mm
Correct Answer: B

8. Maximum percentage error in density when mass, radius, length all have errors:

A) 1%
B) 2%
C) 3%
D) 4%
Correct Answer: D

9. Least count of stop watch = 1/5 s. Time = 25 s. Max % error:

A) 8%
B) 1%
C) 0.8%
D) 16%
Correct Answer: C

10. Vernier callipers LC if N vernier divisions = (N − 1) main scale divisions:

A) N
B) N − 1
C) 1/10N
D) (1/N) − 1
Correct Answer: C

11. Error in P = a³b² / cd when errors are 1%, 2%, 3%, 4%:

A) 10%
B) 7%
C) 4%
D) 14%
Correct Answer: D

12. Equivalent resistance for R₁ = (100 ± 3)Ω, R₂ = (200 ± 4)Ω (series):

A) (300 ± 7)Ω
B) (300 ± 1)Ω
C) (100 ± 7)Ω
D) None
Correct Answer: A

13. Percentage error in R = V/I with V = (100 ± 5)% and I = (100 ± 0.2)%:

A) 5%
B) 2%
C) 7%
D) 3%
Correct Answer: C

14. If units of length and force increased 4×, energy unit:

A) 4×
B) 16×
C) 8×
D) Unchanged
Correct Answer: B

15. Dimensionless physical quantity:

A) Strain
B) Angular velocity
C) Angular momentum
D) Linear momentum
Correct Answer: A

16. Dimensional formula of angular velocity:

A) [MLT⁻¹]
B) [M⁰L⁰T⁻¹]
C) [MLT⁻²]
D) [M⁰L⁰T⁻²]
Correct Answer: D

17. Dimensions of pressure equal:

A) Force per unit volume
B) Energy per unit volume
C) Force
D) Energy
Correct Answer: B

18. Quantity not having dimensions [ML⁻¹T²]:

A) Force
B) Pressure
C) Stress
D) Modulus of elasticity
Correct Answer: A

19. Wrong unit conversion:

A) 1 Å = 10⁻¹⁰ m
B) 1 fermi = 10⁻¹⁵ m
C) 1 light year = 9.46 × 10¹⁵ m
D) 1 AU = 1.496 × 10¹¹ m
Correct Answer: D

20. Quantity with a unit but dimensionless:

A) Strain
B) Reynolds number
C) Angular displacement
D) Poisson’s ratio
Correct Answer: C

21. Which is dimensionless?

A) Force/acceleration
B) Velocity/acceleration
C) Volume/area
D) Energy/work
Correct Answer: D

22. Meaningful operation between A and B of different dimensions:

A) A/B
B) A + B
C) A − B
D) A = B
Correct Answer: A

23. Dimensional analysis applies to:

A) Checking consistency
B) Deducing relations
C) Unit conversion
D) All of these
Correct Answer: D

24. Equating a physical quantity with its dimensional formula gives:

A) Dimensional analysis
B) Dimensional equation
C) Dimensional formula
D) None
Correct Answer: B

25. Dimensions of speed and velocity:

A) [L²T⁻¹], [LT⁻²]
B) [LT⁻¹], [LT⁻²]
C) [LT], [LT]
D) [L⁻¹T], [L⁻¹T⁻¹]
Correct Answer: D

26. Dimensions of force:

A) [ML²T⁻²]
B) [M²LT⁻²]
C) [MLT⁻²]
D) None
Correct Answer: C

27. Significant figures in 4.327 g / 2.51 cm³:

A) 2
B) 4
C) 3
D) 5
Correct Answer: C

28. Sum of 436.32 + 227.2 + 0.301:

A) 663.821
B) 664
C) 663.8
D) 663.8
Correct Answer: B

29. Number of significant figures in 0.00060:

A) 1
B) 2
C) 3
D) 4
Correct Answer: B

30. Most accurate value:

A) 200.0 m
B) 20 × 10¹ m
C) 2 × 10² m
D) 0.2 × 10³ m
Correct Answer: A

Conclusion

Units, dimensions, significant figures and error analysis form the backbone of every calculation and measurement in physics. Whether you are preparing for competitive exams like NEET, JEE or CUET, or simply strengthening your Class 11 fundamentals, mastering these topics ensures precision, clarity and confidence in solving numerical problems. Understanding dimensional formulas helps verify equations, while knowing how errors propagate allows you to interpret experimental data correctly. Concepts such as least count, accuracy, unit conversion, density calculation and identifying dimensionless quantities repeatedly appear in exam patterns.

The 30 MCQs included in this guide cover all essential areas—from dimensional consistency to significant digits and measurement errors—helping you assess your knowledge quickly. With regular practice and conceptual understanding, these questions become easy and intuitive. Focus on the logic behind each answer instead of memorisation, and you’ll find this chapter turning into one of your strongest scoring areas in physics.

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