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Units and Measurements Class 11 Notes for NEET, JEE & CUET (With MCQs and Answers)

If you are preparing for NEET, JEE Main, JEE Advanced, or CUET, then NCERT Class 11 Physics Chapter 1 – Units and Measurements is a must-master chapter. It looks easy, but examiners love to ask tricky questions on significant figures, errors, screw gauge, vernier calipers, and dimensional analysis.

In this post, you’ll get:

  • Short Units and Measurements NCERT Class 11 notes for NEET/JEE

  • A compact formula sheet for Units and Measurements

  • A big collection of Units and Measurements NEET important questions, JEE level problems on units and dimensions, and NEET physics error analysis questions based on the topics students actually struggle with.

Use this as your Units and Measurements mock test for NEET/JEE/CUET and revise before exams.

Quick Notes: Units, Measurements & Errors (For NEET/JEE/CUET)

These short notes are enough for NCERT Physics Chapter 1 Units and Measurements for CUET, NEET and JEE revision.

1. Systems of Units

  • We use SI system in exams:
    Fundamental quantities and units:

    • Length – metre (m)

    • Mass – kilogram (kg)

    • Time – second (s)

    • Current – ampere (A)

    • Temperature – kelvin (K)

    • Amount of substance – mole (mol)

    • Luminous intensity – candela (cd)

2. Least Count & Measuring Instruments

  • Least count (LC) = smallest value a device can measure.

  • Vernier calipers:

    • LC = 1 main scale division (MSD) – 1 vernier scale division (VSD)

  • Screw gauge:

    • Pitch = distance moved in one complete rotation

    • LC = Pitch / (total circular scale divisions)

Important for significant figures class 11 NEET questions and instrument-based problems.

3. Errors & Significant Figures

  • Absolute error = |measured – true|

  • Relative error = absolute error / true value

  • Percentage error = relative error × 100

  • Rules of combining errors:

    • For product/quotient: percentage errors add

    • For power: multiply percentage error by the power.

  • Significant figures ≈ number of reliable digits in a measurement → directly linked to accuracy of measuring instrument.

These are frequently asked as measurement errors NEET MCQs.

4. Dimensional Analysis

  • Every physical quantity can be written as
    [MaLbTcAdΘe…][M^a L^b T^c A^d \Theta^e …]

  • Uses:

    • Check if equation is dimensionally correct

    • Find relation between physical quantities

    • Convert units

  • Many Units and dimensions NEET PYQ with solutions and JEE mains tricks sit here.

Units and Measurements NEET / JEE Important MCQs (With Answers)

Below are mixed-level MCQs: some at NEET level, some as JEE level problems on units and dimensions, and a few that feel like JEE Advanced dimensional analysis challenging questions.

You can directly use them as a Units and Measurements mock test (NEET/JEE) on your quiz app.

A. Screw Gauge & Vernier Calipers – Instrument Based MCQs

Q1. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The circular scale has 50 divisions. The screw gauge has a zero error of –0.03 mm.
While measuring the diameter of a thin wire, a student notes:

  • Main scale reading = 3.0 mm

  • Circular scale reading = 3.5 divisions

The diameter of the wire is:

(a) 3.32 mm
(b) 3.72 mm
(c) 3.67 mm
(d) 3.38 mm

Answer: (d)

Q2. A screw gauge gives the following reading for the diameter of a wire:

  • Main scale reading: 0 mm

  • Circular scale reading: 52 divisions
    Given that 1 mm on main scale corresponds to 100 divisions of circular scale. The diameter of the wire is:

(a) 0.052 cm
(b) 0.026 cm
(c) 0.005 cm
(d) 0.52 cm

Answer: (a)
(Hint: LC = 0.01 mm = 0.001 cm, reading = 52 × 0.001 = 0.052 cm)

Q3. A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he most likely use?

(a) Meter scale
(b) Vernier calipers (10 vernier divisions = 9 main scale divisions, and 10 MSD = 1 cm)
(c) Screw gauge with 100 divisions on circular scale and pitch 1 mm
(d) Screw gauge with 50 divisions on circular scale and pitch 1 mm

Answer: (b)

Q4. A screw gauge of pitch 0.5 mm is used to measure the diameter of a uniform wire of length 6.8 cm. The readings are:

  • Main scale reading = 1.5 mm

  • Circular scale reading = 7 divisions
    Screw gauge has 50 divisions on circular scale. The curved surface area of the wire, to appropriate significant figures, is:

(a) 6.8 cm²
(b) 3.4 cm²
(c) 3.9 cm²
(d) 2.4 cm²

Answer: (b)

Q5. In a vernier calipers, each cm on main scale is divided into 20 equal parts. If the 10th vernier division coincides with the 9th main scale division, the vernier constant (VC) is ______ × 10⁻² mm.

(a) 5 × 10⁻² mm
(b) 10 × 10⁻² mm
(c) 0.05 × 10⁻² mm
(d) 9 × 10⁻² mm

Answer: (a)

Q6. A student measures the diameter of a small steel ball using a screw gauge of least count 0.001 cm.

  • Main scale reading = 5 mm

  • Circular scale coincides at 25 divisions
    Zero error of screw gauge = –0.004 cm.
    The correct diameter of the ball is:

(a) 0.053 cm
(b) 0.525 cm
(c) 0.521 cm
(d) 0.529 cm

Answer: (c)

B. Error Analysis & Significant Figures – NEET Physics Error Questions

Q7. When voltage and current in a conductor are measured as (100 ± 4)V and (5 ± 0.2)A, the percentage error in the calculation of resistance R = V/I is:

(a) 8%
(b) 4%
(c) 20%
(d) 10%

Answer: (a)

Q8. If the error in measuring the radius of a sphere is 1%, the error in its volume is:

(a) 1.10%
(b) 3%
(c) 5%
(d) 8%

Answer: (b)
(Hint: V ∝ r³ → error = 3 × 1% = 3%)

Q9. A force F is applied on a square plate of side L. If the percentage error in L is 2% and that in F is 4%, the permissible error in pressure P = F/L² is:

(a) 2%
(b) 4%
(c) 6%
(d) 8%

Answer: (d)
(Hint: P ∝ F/L² → ΔP% = 4% + 2×2% = 8%)

Q10. The percentage errors in measurement of mass and speed are 1% and 2% respectively. The percentage error in kinetic energy (½mv²) is:

(a) 5%
(b) 2.5%
(c) 3%
(d) 1.5%

Answer: (a)

Q11. The side of a cubical block measured with a vernier calipers is 2.50 cm. The vernier constant is 0.01 cm. The maximum possible error in the area of one side is:

(a) ±0.01 cm²
(b) ±0.02 cm²
(c) ±0.05 cm²
(d) ±0.10 cm²

Answer: (c)

Q12. A public park in the form of a square has an area (100 ± 0.2) m². The side of the park is:

(a) (10 ± 0.01) m
(b) (10 ± 0.1) m
(c) (10.0 ± 0.1) m
(d) (10.0 ± 0.2) m

Answer: (a)

Q13. Dimensional formula of a physical quantity X is [M⁻¹L³T⁻²]. Errors in measuring M, L and T are 2%, 3% and 4% respectively. Maximum percentage error in X is:

(a) 9%
(b) 10%
(c) 14%
(d) 19%

Answer: (d)
(Hint: ΔX% = |–1|×2% + 3×3% + |–2|×4% = 2 + 9 + 8 = 19%)

Q14. If absolute errors in two physical quantities A and B are a and b respectively, then the absolute error in (A – B) is:

(a) a – b
(b) b – a
(c) a = b
(d) a + b

Answer: (d)

Q15. The resistance R = V/I, where V = (100 ± 5)V and I = (10 ± 0.2)A. The percentage error in R is:

(a) 5.20%
(b) 4.80%
(c) 7%
(d) 3%

Answer: (c)

Q16. The density of a material (cube) is determined from mass and length. If relative errors in mass and length are 1.5% and 1% respectively, the maximum error in density is:

(a) 2.5%
(b) 3.5%
(c) 4.5%
(d) 6%

Answer: (c)
(Hint: ρ = m/L³ → Δρ% = 1.5% + 3×1% = 4.5%)

Q17. A body weighs 22.42 g and has volume 4.7 cc. Possible errors in mass and volume are 0.01 g and 0.1 cc. The maximum error in density is:

(a) 22%
(b) 2%
(c) 0.20%
(d) 0.02%

Answer: (b)

Q18. The resistance R = V/I where V = (50 ± 2)V and I = (20 ± 0.2)A. The percentage error in R is x%. The value of x (nearest integer) is:

(a) 5
(b) 0.5
(c) 0.05
(d) 50

Answer: (a)

Q19. The period of a simple pendulum is
T = 2π √(L/g).
Measured length L = 1.0 m (LC = 1 mm) and time for one oscillation is 1.95 s (stopwatch resolution = 0.01 s). The percentage error in g is:

(a) 1.13%
(b) 1.03%
(c) 1.33%
(d) 1.30%

Answer: (a)

Q20. If length and time period of a pendulum have errors of 1% and 3% respectively, the error in g is:

(a) 4%
(b) 5%
(c) 6%
(d) 7%

Answer: (d)
(Hint: g ∝ L/T² → Δg% = 1% + 2×3% = 7%)

Q21. Maximum errors in measuring resistance, current and time in a circuit are 1%, 2% and 3% respectively. The maximum percentage error in heat dissipated (H ∝ I²RT) is:

(a) 2%
(b) 4%
(c) 6%
(d) 8%

Answer: (d)
(Hint: H ∝ I² R T → 2×2% + 1% + 3% = 8%)

Q22. For z = a² x³ y¹ᐟ² (a is constant). If percentage errors in x and y are 4% and 12% respectively, percentage error in z is:

(a) 18%
(b) 12%
(c) 6%
(d) 3%

Answer: (a)
(Hint: z ∝ x³ y¹ᐟ² → Δz% = 3×4% + ½×12% = 12 + 6 = 18%)

Q23. Assertion–Reason
Assertion (A): The number of significant figures depends on the least count of measuring instrument.
Reason (R): Significant figures define the accuracy of measuring instrument.

(a) Both A and R are correct and R is correct explanation of A.
(b) Both A and R are correct, but R is not correct explanation of A.
(c) A is correct but R is incorrect.
(d) Both A and R are incorrect.

Answer: (b)

Q24. Assertion–Reason
Assertion (A): Number of significant figures in 0.005 is one and in 0.500 is three.
Reason (R): This is because zeros are not significant.

(a) Both A and R are true and R is correct explanation of A.
(b) Both A and R are true but R is not correct explanation of A.
(c) A is true but R is false.
(d) Both A and R are false.

Answer: (c)

C. Dimensional Analysis – JEE Level Problems on Units and Dimensions

Q25. Which pair of physical quantities does not have same dimensions?

(a) Pressure and stress
(b) Tension and surface tension
(c) Strain and angle
(d) Energy and work

Answer: (b)

Q26. Dimensional formula of Farad (capacitance) is:

(a) [M⁻¹L⁻²TQ]
(b) [M⁻¹L⁻²T²Q²]
(c) [M⁻¹L⁻²TQ²]
(d) [M⁻¹L⁻²T²Q]

Answer: (b)

Q27. The pair of quantities having same dimensions is:

(a) Impulse and surface tension
(b) Angular momentum and work
(c) Work and torque
(d) Young’s modulus and energy

Answer: (c)

Q28. The dimensions of angular momentum / magnetic moment are:

(a) [M A⁻¹ T⁻¹]
(b) [M⁻¹ A T⁻¹]
(c) [M A T⁻¹]
(d) [M A⁻¹ T]

Answer: (a)

Q29. Which physical quantity does not have dimensional formula [ML⁻¹T⁻²]?

(a) Force
(b) Pressure
(c) Stress
(d) Modulus of elasticity

Answer: (a)

Q30. Dimensional formula of thermal conductivity is:

(a) [M L T⁻¹ θ⁻¹]
(b) [M L T⁻³ θ⁻¹]
(c) [M L T⁻³ θ⁻²]
(d) [M L² T⁻² θ]

Answer: (b)

Q31. [M L² T⁻³] represents the dimensions of:

(a) Pressure
(b) Energy
(c) Power
(d) Force

Answer: (c)

Q32. Which of the following can be written as kg·m²·A⁻²·T⁻²?

(a) Inductance
(b) Reactance
(c) Capacitance
(d) Resistance

Answer: (a)

Q33. The dimension of magnetic field B in M, L, T and C (coulomb) is:

(a) [M L T⁻¹ C⁻¹]
(b) [M T⁻² C⁻¹]
(c) [M T² C⁻²]
(d) [M T⁻¹ C⁻¹]

Answer: (d)

Q34. The dimensions of Reynolds number are:

(a) [M⁰L⁻¹T⁻¹]
(b) [M⁰L⁰T⁰]
(c) [M¹L⁰T⁻²]
(d) [M¹L⁻²T⁻¹]

Answer: (b)

Q35. Out of the following pairs, which one does not have same dimensions?

(a) Angular momentum and Planck’s constant
(b) Impulse and momentum
(c) Moment of inertia and moment of force
(d) Work and torque

Answer: (c)

Q36. Dimensions of (μ₀ ε₀)⁻¹ᐟ² are:

(a) [L¹ᐟ² T⁻¹ᐟ²]
(b) [L⁻¹ T]
(c) [L T⁻¹]
(d) [L¹ᐟ² T¹ᐟ²]

Answer: (c)
(Hint: It has same dimension as speed of light)

Q37. The ratio of dimensions of Planck’s constant to moment of inertia is dimension of:

(a) Frequency
(b) Velocity
(c) Angular momentum
(d) Time

Answer: (a)

Q38. Dimensional formula for coefficient of restitution is:

(a) M L T⁻²
(b) M⁰L⁰T⁰
(c) M L T⁻¹
(d) M T⁻²

Answer: (b) (dimensionless)

Q39. If force (F), work (W) and velocity (v) are taken as fundamental quantities, the dimensional formula of time (T) is:

(a) [W F v]
(b) [W F v⁻¹]
(c) [W⁻¹ F⁻¹ v]
(d) [W F⁻¹ v⁻¹]

Answer: (d)

Q40. The dimension of stopping potential V₀ in photoelectric effect in terms of Planck’s constant h, speed of light c, gravitational constant G and ampere A is:

(a) [h²ᐟ³ c¹ᐟ³ G⁴ᐟ³ A⁻¹]
(b) [h⁰ G⁻¹ c⁵ A⁻¹]
(c) [h² G³ᐟ² c¹ᐟ³ A⁻¹]
(d) [h²ᐟ³ c⁵ᐟ³ G¹ᐟ³ A⁻¹]

Answer: (b)

D. Mixed Conceptual & Conversion Questions

Q41. A material has density 128 kg m⁻³ in SI units. In a new system where unit length = 25 cm and unit mass = 50 g, the numerical value of density is:

(a) 40
(b) 16
(c) 640
(d) 410

Answer: (a)

Q42. Assertion–Reason
Assertion (A): In five complete rotations of circular scale, a screw gauge moves 5 mm on main scale and has 50 divisions on circular scale, then least count is 0.001 cm.
Reason (R): Least count = Pitch / (Total divisions on circular scale).

(a) Both A and R correct and R explains A
(b) Both A and R correct but R does not explain A
(c) A correct, R not correct
(d) A not correct, R correct

Answer: (d)

Q43. Which of the following statements is incorrect?

(a) Every measurement by any measuring instrument has some error.
(b) Every calculated physical quantity based on measured values has some error.
(c) A measurement can have more accuracy but less precision and vice versa.
(d) Percentage error is different from relative error.

Answer: (d) (They are same, just ×100)

There were also some Match the List and dimensionally correct / incorrect equation questions in your list – you can add them as a separate “Advanced Practice” section if you like, but this post is already long enough for one chapter revision.

How to Use This Blogpost for Exam Prep

  • First read the short notes – this covers theory for Physics Class 11 Chapter 1 short notes for NEET.

  • Then attempt the MCQs without looking at answers as a mini Units and Measurements mock test for NEET/JEE.

  • Mark questions you got wrong and revise related theory – especially significant figures, error propagation and dimensional analysis JEE mains tricks.

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