AFNS Physics Chapter 01# Measurements
1:Physical Quantities and SI Units
In Physics, every measurement has two parts: a number and a unit. For example, if someone says ‘the table is 2 metres long’ — 2 is the number and metre is the unit. Without units, a measurement is meaningless.
1.1 Types of Physical Quantities
KEY CONCEPT: Physical quantities are divided into two types: Base Quantities (7 fundamental quantities) and Derived Quantities (formed by combining base quantities).
Base Quantities
These are the fundamental quantities that cannot be expressed in terms of other quantities. There are exactly 7 SI base quantities:
| Base Quantity | SI Unit | Symbol |
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric Current | ampere | A |
| Temperature | kelvin | K |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
QUICK TIP: In AFNS MCQs the most common trick is mixing up units. Remember: kilogram is for MASS (not weight), kelvin is for TEMPERATURE (not Celsius), candela is for LUMINOUS INTENSITY.
Derived Quantities
These are obtained by combining base quantities through multiplication or division. You do NOT need to memorise them separately — just know the formula.
| Derived Quantity | Formula | SI Unit |
| Speed | Length / Time | m/s |
| Acceleration | Velocity / Time | m/s² |
| Force | Mass × Acceleration | kg·m/s² = Newton (N) |
| Work / Energy | Force × Distance | N·m = Joule (J) |
| Power | Work / Time | J/s = Watt (W) |
| Pressure | Force / Area | N/m² = Pascal (Pa) |
| Density | Mass / Volume | kg/m³ |
| Electric Charge | Current × Time | A·s = Coulomb (C) |
| Frequency | 1 / Time Period | 1/s = Hertz (Hz) |
EXAMPLE: Force has SI unit Newton. Newton = kg·m/s². So if asked ‘What are the base units of Force?’ the answer is kg·m·s⁻².
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Scientific Notation and SI Prefixes
In Physics we deal with very large numbers (like the speed of light = 300,000,000 m/s) and very small numbers (like electron mass = 0.00000000000000000000000000000091 kg). Scientific notation makes these easy to write and compare.
2.1 Scientific Notation
KEY CONCEPT: Scientific notation: A × 10ⁿ, where 1 ≤ A < 10 and n is a positive or negative integer.
EXAMPLE: Speed of light = 3.0 × 10⁸ m/s | Electron mass = 9.1 × 10⁻³¹ kg | Diameter of atom = 1.0 × 10⁻¹⁰ m
2.2 SI Prefixes (Must Memorize)
Instead of writing 10⁻³ every time, we use prefixes like milli (m). These are extremely important for AFNS MCQs.
| Prefix | Symbol | Power of 10 | Example |
| Tera | T | 10¹² | 1 THz = 10¹² Hz |
| Giga | G | 10⁹ | 1 GHz = 10⁹ Hz |
| Mega | M | 10⁶ | 1 MHz = 10⁶ Hz |
| kilo | k | 10³ | 1 km = 10³ m |
| hecto | h | 10² | 1 hm = 100 m |
| deci | d | 10⁻¹ | 1 dm = 0.1 m |
| centi | c | 10⁻² | 1 cm = 0.01 m |
| milli | m | 10⁻³ | 1 mm = 0.001 m |
| micro | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico | p | 10⁻¹² | 1 pm = 10⁻¹² m |
QUICK TIP: Memory trick for order: ‘The Great Man Keeps His Desk Clean Making Nice Pots’ = Tera, Giga, Mega, Kilo, Hecto, Deca, Centi, Milli, Nano, Pico
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Significant Figures
Significant figures (sig figs) show how precise a measurement is. Every digit that is reliably known plus one uncertain digit is significant.
3.1 Rules for Counting Significant Figures
- All non-zero digits are significant. Example: 4567 → 4 sig figs
- Zeros between non-zero digits are significant. Example: 4007 → 4 sig figs
- Leading zeros are NOT significant. Example: 0.0045 → 2 sig figs
- Trailing zeros AFTER a decimal point are significant. Example: 3.400 → 4 sig figs
- Trailing zeros in a whole number are ambiguous unless a decimal point is shown. Example: 500 → unclear; 500. → 3 sig figs
EXAMPLE: How many sig figs in 0.0050300? Answer: 5 (leading zeros don’t count; 5, 0, 3, 0, 0 after the first non-zero digit are all significant)
3.2 Calculations with Significant Figures
KEY CONCEPT: Addition/Subtraction: Round answer to fewest DECIMAL PLACES. Multiplication/Division: Round answer to fewest SIGNIFICANT FIGURES.
EXAMPLE: Addition: 12.5 + 1.234 = 13.734 → round to 1 decimal place → 13.7 | Multiplication: 4.5 × 2.34 = 10.53 → 2 sig figs → 11
QUICK TIP: AFNS shortcut: In division/multiplication questions, always count sig figs in each given value. Your answer cannot be more precise than your least precise measurement.
3.3 Rounding Rules
- If the digit to be dropped is less than 5 → round down (keep previous digit same)
- If the digit to be dropped is 5 or more → round up (increase previous digit by 1)
EXAMPLE: Round 3.465 to 2 decimal places: digit after 6 is 5 → round up → 3.47
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Errors in Measurements
No measurement is 100% perfect. The difference between the measured value and the true value is called error. Understanding errors is essential for accurate scientific work.
4.1 Types of Errors
(a) Systematic Errors
These errors always push the result in the same direction — always too high or always too low. They are caused by faults in the instrument or method.
- Zero error in instruments (e.g., a ruler that does not start from exactly zero)
- Poorly calibrated instruments
- Environmental effects (e.g., temperature affecting a metal ruler)
KEY CONCEPT: Systematic errors cannot be reduced by repeating the experiment. They must be identified and corrected.
(b) Random Errors
These errors are unpredictable and can push the result either too high or too low. They are caused by limitations of the measuring instrument or the observer.
- Observer’s reaction time in timing experiments
- Parallax error while reading a scale
- Slight variations in experimental conditions
KEY CONCEPT: Random errors can be reduced by repeating the experiment many times and taking the average (mean) of readings.
4.2 Accuracy vs Precision
| Accuracy | Precision |
| How close a measurement is to the TRUE value | How close repeated measurements are to EACH OTHER |
| Affected by systematic errors | Affected by random errors |
| Example: Hitting the bullseye on a dartboard | Example: All darts landing close together (even if not bullseye) |
QUICK TIP: Classic AFNS question: ‘A student gets 9.8, 9.7, 9.9 for g but true value is 9.81 — is this accurate or precise?’ Answer: Both accurate AND precise!
4.3 Absolute, Relative and Percentage Error
- Absolute Error = |Measured Value − True Value|
- Relative Error = Absolute Error / True Value
- Percentage Error = Relative Error × 100%
EXAMPLE: True value of g = 9.81 m/s², Measured value = 9.75 m/s² | Absolute error = |9.75 − 9.81| = 0.06 | Percentage error = (0.06/9.81) × 100 = 0.61%.
Q51. Which pair has the same dimensions?
- (A) Work and Power
- (B) Force and Momentum
- (C) Work and Torque
- (D) Pressure and Density
Answer: (C) Work and Torque
Explanation: Both Work and Torque = Force × Distance = [ML²T⁻²]. They have the same dimensions.
Q52. Dimension of Planck’s constant h (E = hf) is:
- (A) [MLT]
- (B) [ML²T⁻¹]
- (C) [ML²T⁻²]
- (D) [ML⁻¹T⁻¹]
Answer: (B) [ML²T⁻¹]
Explanation: h = E/f = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. This is also the dimension of angular momentum.
Q53. Dimensional analysis CANNOT determine:
- (A) dimensions of a constant
- (B) numerical values of constants
- (C) consistency of an equation
- (D) units of a derived quantity
Answer: (B) numerical values of constants
Explanation: Dimensional analysis can check formula consistency and derive relations but CANNOT give numerical values of dimensionless constants.
Q54. The dimension [ML²T⁻²] corresponds to:
- (A) power
- (B) impulse
- (C) kinetic energy
- (D) pressure
Answer: (C) kinetic energy
Explanation: KE = ½mv² = [M][L²T⁻²] = [ML²T⁻²]. Power = [ML²T⁻³] and pressure = [ML⁻¹T⁻²].
Q55. Force × Time has dimensions of:
- (A) energy
- (B) momentum
- (C) power
- (D) pressure
Answer: (B) momentum
Explanation: Force × Time = [MLT⁻²][T] = [MLT⁻¹] = dimensions of momentum (also called impulse).
Q56. Which quantity has dimensions [L²]?
- (A) volume
- (B) area
- (C) density
- (D) length
Answer: (B) area
Explanation: Area = length × width = [L][L] = [L²].
Q57. The SI unit of impulse is the same as:
- (A) joule
- (B) watt
- (C) newton-second
- (D) pascal
Answer: (C) newton-second
Explanation: Impulse = Force × time = N·s. This equals the unit of momentum (kg·m/s = N·s).
Section E: Measuring Instruments (Q58–75)
Q58. The least count of a Vernier Caliper is:
- (A) 0.1 mm
- (B) 0.01 mm
- (C) 1 mm
- (D) 0.001 mm
Answer: (A) 0.1 mm
Explanation: Standard Vernier Caliper: 1 MSD = 1 mm, 10 VSD = 9 mm, so 1 VSD = 0.9 mm. LC = 1 − 0.9 = 0.1 mm.
Q59. The least count of a Screw Gauge is:
- (A) 0.1 mm
- (B) 0.01 mm
- (C) 1 mm
- (D) 0.001 mm
Answer: (B) 0.01 mm
Explanation: Screw Gauge: Pitch = 0.5 mm, circular scale divisions = 50. LC = 0.5/50 = 0.01 mm.
Q60. A Vernier caliper main scale reads 2.3 cm and vernier scale 6th division coincides. The reading is:
- (A) 2.36 cm
- (B) 2.306 cm
- (C) 2.36 mm
- (D) 2.6 cm
Answer: (A) 2.36 cm
Explanation: Reading = 2.3 + (6 × 0.01) = 2.3 + 0.06 = 2.36 cm.
Q61. The pitch of a screw gauge is:
- (A) distance between two adjacent threads
- (B) distance moved per complete rotation
- (C) the least count
- (D) the zero error
Answer: (B) distance moved per complete rotation
Explanation: Pitch = linear distance moved by the thimble in one complete rotation = 0.5 mm (standard).
Q62. A positive zero error in a screw gauge means the instrument reads:
- (A) less than actual value
- (B) more than actual value
- (C) exactly actual value
- (D) zero always
Answer: (B) more than actual value
Explanation: Positive zero error means instrument over-reads. To correct: subtract the zero error from the reading.
Q63. Vernier calipers can be used to measure:
- (A) mass of an object
- (B) external diameter of a cylinder
- (C) temperature
- (D) electrical resistance
Answer: (B) external diameter of a cylinder
Explanation: Vernier calipers measure lengths — external diameter, internal diameter, and depth.
Q64. The number of divisions on the vernier scale of a standard vernier caliper is:
- (A) 5
- (B) 10
- (C) 50
- (D) 100
Answer: (B) 10
Explanation: Standard Vernier Caliper has 10 divisions on the vernier scale, each = 0.9 mm.
Q65. If zero error of screw gauge is +0.03 mm and raw reading is 5.67 mm, the correct reading is:
- (A) 5.70 mm
- (B) 5.64 mm
- (C) 5.67 mm
- (D) 5.97 mm
Answer: (B) 5.64 mm
Explanation: Correct reading = Raw reading − Zero error = 5.67 − 0.03 = 5.64 mm.
Q66. Which instrument is more precise — Vernier Caliper or Screw Gauge?
- (A) Vernier Caliper (LC = 0.1 mm)
- (B) Screw Gauge (LC = 0.01 mm)
- (C) Both are equally precise
- (D) Depends on the measurement
Answer: (B) Screw Gauge (LC = 0.01 mm)
Explanation: Smaller least count = greater precision. Screw Gauge (0.01 mm) is 10 times more precise than Vernier Caliper (0.1 mm).
Q67. Screw Gauge is also known as:
- (A) Travelling microscope
- (B) Micrometer screw gauge
- (C) Spherometer
- (D) Barometer
Answer: (B) Micrometer screw gauge
Explanation: The full name is micrometer screw gauge. It measures in the order of micrometres (10⁻⁶ m).
Q68. In a Vernier caliper, if 9 main scale divisions = 10 vernier scale divisions, then LC =
- (A) 0.9 mm
- (B) 0.01 cm
- (C) 0.1 mm
- (D) Both B and C
Answer: (D) Both B and C
Explanation: LC = 1 MSD − 1 VSD = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm. Both (B) and (C) are equal.
Q69. A screw gauge has 0 on the circular scale below the reference line when jaws are closed. This means:
- (A) positive zero error
- (B) negative zero error
- (C) no zero error
- (D) instrument is defective
Answer: (B) negative zero error
Explanation: If zero mark is BELOW reference line, the gauge under-reads → negative zero error. Correction: add the zero error to the reading.
Q70. Least count error is:
- (A) a systematic error
- (B) a random error
- (C) the smallest reliable measurement
- (D) the largest error
Answer: (C) the smallest reliable measurement
Explanation: Least count is the smallest scale division the instrument can read — it represents the precision limit of the instrument.
Q71. Which of the following measures the thickness of a glass plate most accurately?
- (A) Ruler
- (B) Tape measure
- (C) Vernier Caliper
- (D) Screw Gauge
Answer: (D) Screw Gauge
Explanation: For very thin objects like glass plates, Screw Gauge (LC = 0.01 mm) gives the most accurate reading.
Q72. The main scale of a screw gauge reads 3 mm. Thimble reads 25 and LC = 0.01 mm. Correct reading?
- (A) 3.25 mm
- (B) 3.025 mm
- (C) 3.25 cm
- (D) 25.3 mm
Answer: (A) 3.25 mm
Explanation: Reading = Main scale + (Thimble × LC) = 3.0 + (25 × 0.01) = 3.0 + 0.25 = 3.25 mm.
Q73. How many types of zero error exist in a Screw Gauge?
- (A) 1
- (B) 2
- (C) 3
- (D) 4
Answer: (B) 2
Explanation: Two types: Positive zero error (circular scale reads above zero) and Negative zero error (reads below zero).
Q74. The range of a standard laboratory Vernier Caliper is typically:
- (A) 0–1 cm
- (B) 0–10 cm
- (C) 0–15 cm
- (D) 0–25 cm
Answer: (C) 0–15 cm
Explanation: Standard lab Vernier Calipers have a range of 0 to 15 cm (150 mm).
Q75. Which of the following is NOT a use of the Vernier Caliper?
- (A) Measuring external diameter
- (B) Measuring internal diameter
- (C) Measuring depth of a hole
- (D) Measuring mass of an object
Answer: (D) Measuring mass of an object
Explanation: Vernier Caliper measures lengths only (external, internal, depth). Mass is measured with a balance.
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