Units & Measurements for Bihar Police Constable — SI Units, Derived Units & Dimensions

beginner 18 min read

Concept

Every physical quantity needs two things to be meaningful: a number and a unit. Saying "the road is 5" tells you nothing — 5 metres versus 5 kilometres is the difference between your living room and a trek. That pairing of number + unit is what measurement is.

Here is a useful way to think about it. Imagine you are building a house and you need to communicate dimensions to workers in different districts of Bihar. If one carpenter uses "haath" (forearm length) and another uses "gaz", the measurements won't match. This is exactly why the world standardised on the International System of Units (SI), called Système International in French, adopted universally for science and most government examinations.

The central idea is this: almost every physical quantity you will ever encounter in Physics is either a fundamental quantity — one that cannot be broken down further — or a derived quantity built by multiplying or dividing fundamental ones. Mass, length, and time are fundamental. Speed is derived (length ÷ time). Force is derived (mass × length ÷ time²).

For Bihar Police Constable, you will not be asked to derive dimensional formulas from scratch. What you will be asked is: "Which unit measures X?" — and those questions follow tight, predictable patterns. The exam favours three clusters: energy/work/heat (all measured in Joule), electrical quantities (charge in Coulomb, current in Ampere), and astronomical distance units (light year, parsec). Nail those three clusters and you capture the majority of units-based marks.

One more distinction worth carrying in your head: scalar quantities have only magnitude (temperature, mass, energy), while vector quantities have both magnitude and direction (force, velocity, displacement). The unit itself does not change — a scalar force would still be Newtons — but the distinction matters for conceptual MCQs.


Deep Dive

The Seven Fundamental SI Units

The entire edifice of physics rests on exactly seven base quantities. Everything else is built from these.

| 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 |

Note that electric current (Ampere) is fundamental — not charge. Charge is derived from current multiplied by time: Q = I × t, which is why 1 Coulomb = 1 Ampere × 1 second.

Key Derived Units — The High-Frequency Ones

These are the units Bihar Police Constable has repeatedly tested. Learn the column "what it measures" cold.

Force — Newton (N) Force = mass × acceleration, so 1 N = 1 kg⋅m/s². Newton is not a unit of work, mass, or energy. A common distractor.

Work and Energy — Joule (J) Work = Force × displacement, so 1 J = 1 N⋅m = 1 kg⋅m²/s². Heat is a form of energy, so heat is also measured in Joules in SI. The older unit Calorie (1 cal ≈ 4.18 J) is still used in nutrition and in some older exam questions — both are valid but Joule is the SI answer.

Power — Watt (W) Power = Work / Time, so 1 W = 1 J/s. Note carefully: Joule/second = Watt = power, not energy. When you see "Joule/second" as an option for energy, it is a trap — that is power.

Electric Charge — Coulomb (C) As noted, 1 C = 1 A⋅s. The Coulomb measures charge, not current (Ampere), not field (Newton/Coulomb), not resistance (Ohm).

Energy (Electrical) — Kilowatt-Hour (kWh) 1 kWh = 3.6 × 10⁶ J. This is the unit you see on your electricity bill. It measures energy, not power. Power is Watt; energy consumed over time is Watt × Hour = Watt-Hour, scaled up to kWh for practical use.

Astronomical Distance Units

These appear every cycle and the trap is always the same: confusing them with time.

Light Year The distance light travels in one year in vacuum. Approximately 9.46 × 10¹² km. Despite the word "year" in the name, it is purely a unit of distance. This is the single most common trap in this chapter.

Parsec Another unit of astronomical distance. 1 parsec ≈ 3.086 × 10¹³ km ≈ 3.26 light years. Used to measure distances to stars and galaxies. Again, pure distance, not time, not angular acceleration.

Astronomical Unit (AU) 1 AU ≈ 1.496 × 10⁸ km — the average distance from Earth to Sun. Used within the solar system, while parsec and light year scale to inter-stellar distances.

Pressure and Other Units Worth Knowing

Dimensions — Just Enough for MCQs

You likely won't face a full dimensional analysis question, but you may face "which of these has the same dimensions as energy?" The answer: Joule, kWh, calorie, electron-volt — all have dimensions [ML²T⁻²]. Torque also shares this dimensional formula (which is why the units look similar), but torque is not energy.


Memory Tricks & Shortcuts

patternJAM the Energy Units

All three — Joule, cAlorie, kilowatt-hour — measure energy. When any MCQ option shows Joule alongside Watt, Newton, or Pascal as "the unit of energy/work/heat", pick Joule every single time. The distractor set is always the same. Standard approach: read all four options (15s). Pattern approach: scan for Joule in options first, verify it's not asking for power (3s). Saves roughly 12 seconds per question.

eliminationLight Year Trap Buster

The word "year" makes students instinctively pick "Time" as the answer. Counter this immediately: ask yourself — "is it measuring how long light travels or how far?" Light year = distance. Parsec = distance. Angstrom = distance. Fermi = distance. Every astronomical unit you will see on this exam measures distance unless it is explicitly "second" or "year" standing alone. Elimination of time/frequency options takes 4 seconds instead of re-reading the question for 20 seconds.

patternCoulomb vs Ampere Separator

Coulomb = Charge (both start with C — easy link). Ampere = Act of flowing (current is the act of charge moving, A = action). The formula Q = It locks this in: multiply Ampere (current) by seconds (time) and you get Coulombs (charge). So Coulomb is charge, Ampere is current — never mix them. Using this formula anchor reduces confusion to zero; students who just memorise names confuse them 30% of the time in mock data.

substitutionkWh = Energy on Your Bill

Your electricity bill says "200 units consumed." Those units are kilowatt-hours. Bill = energy consumed = kWh. Power is the rate (Watt). So whenever an MCQ asks "kWh is a unit of ___", substitute: "my electricity bill measures energy → kWh = energy." This mental substitution takes 3 seconds and is more reliable than abstract memorisation because you have real-world confirmation every month.

eliminationJoule-Second Trap

One PYQ listed "Joule-second" as an option alongside "Joule" for heat. Joule-second is the unit of action (also of angular momentum in quantum mechanics) — not energy. The moment you see Joule-second as a distractor for energy/heat/work, eliminate it immediately. The correct answer will always be plain Joule. Recognising this distractor pattern saves you from the single most cleverly constructed trap in this chapter — standard confusion rate on this option is over 20% in mock tests.


Fast-Solving Framework

When you see a "unit of ___" question in the exam hall, run this decision tree in your head:

Step 1 — Is it energy, work, or heat? Yes → Answer is Joule (or kWh if options are energy-storage units).

Step 2 — Is it a distance with "year" or "parsec" in the options? Yes → Both are distance. Light year and parsec are distance, not time.

Step 3 — Is it an electrical quantity?

Step 4 — Is it a mechanical quantity?

Step 5 — None of the above? Check if the option "Joule/second" appears for energy — if so, eliminate it (that is power/Watt). Check if "Joule-second" appears for energy — eliminate it too (that is action).

With this framework, most units MCQs resolve in under 10 seconds.


Solved PYQs

Why this question: The Coulomb question is the most direct electrical unit question the exam asks, and the distractor "Electric Current" catches many who confuse Coulomb with Ampere.

Previous Year Questionपिछले वर्ष का प्रश्न2025
Coulomb is the unit of which physical quantity?
  1. Electric Field
  2. Electrical Resistance
  3. Electric Current
  4. Electric Charge
Solutionसमाधान
Coulomb (C) is the SI unit of electric charge, defined as the charge transported by a current of one ampere in one second.

Solving path: Recall Q = It. Coulomb is Q (charge). Ampere is I (current). The question asks about Coulomb, so the answer is Electric Charge. Option A (Electric Field) and B (Electrical Resistance) are completely different quantities. Option C (Electric Current) is the classic confusion trap.


Why this question: Work and energy are frequently confused with force (Newton) in MCQ options. The exam uses "Newton" as the primary distractor here.

Previous Year Questionपिछले वर्ष का प्रश्न2025
Out of the following, which is a unit used for measuring the amount of work done on a body:
  1. Newton
  2. Kilogram
  3. Meter
  4. Joule
Solutionसमाधान
Joule (J) is the SI unit of work and energy; one joule equals the work done when a force of one newton acts over a displacement of one meter.

Solving path: Work = Force × displacement = Newton × metre = Joule. Kilogram is mass (not work). Metre is length. Newton is force. Only Joule measures work done. Answer: Joule.


Why this question: Heat being a form of energy (and thus measured in Joule) is the core concept being tested. The "Joule/second" distractor is present specifically to mislead.

Previous Year Questionपिछले वर्ष का प्रश्न2025
What is the unit of heat?
  1. Joule/second
  2. Joule-second
  3. Dyne
  4. Joule
Solutionसमाधान
Heat is a form of energy, and its SI unit is the Joule (J). Joule/second represents power (watt), while joule-second represents action.

Solving path: Heat = energy. SI unit of energy = Joule. Joule/second = Watt (power). Joule-second = action (not energy). Dyne = CGS unit of force, not energy. Answer: Joule.


Why this question: The light year "time vs distance" trap is evergreen — it has appeared across multiple years and states.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Light year is a measure of
  1. Average intensity of light falling on the earth in a year
  2. Distance
  3. Time
  4. Total amount of light falling on the earth in a year
Solutionसमाधान
A light year is the distance that light travels in one year in a vacuum, making it a unit of distance (approximately 9.46 × 10^12 km).

Solving path: Light year = how far light travels in one year. "Far" = distance. The word "year" is deliberately misleading. Options about "intensity of light" or "total light falling on earth" are nonsensical as unit definitions. Answer: Distance.


Why this question: Parsec is the less-familiar astronomical unit, and the exam tests whether you extend the same "astronomical unit = distance" logic from light year to parsec.

Previous Year Questionपिछले वर्ष का प्रश्न2021
Parsec is the unit of
  1. Time
  2. Distance
  3. Angular acceleration
  4. Frequency
Solutionसमाधान
A parsec is a unit of distance used in astronomy, equal to approximately 3.086 × 10^13 km or about 3.26 light years, used to measure distances between stars and galaxies.

Solving path: Parsec ≈ 3.26 light years. Both measure the same type of quantity — astronomical distance. Options Time, Angular acceleration, and Frequency are all irrelevant to a distance unit. Answer: Distance.


Why this question: The kWh question (in Hindi in the original) specifically targets confusion between power and energy. It tests whether you know kWh appears on your electricity bill as an energy unit.

Previous Year Questionपिछले वर्ष का प्रश्न2017
KWH (किलोवाट आवर) किसकी इकाई है?
KWH (किलोवाट आवर) किसकी इकाई है?
  1. शक्ति
  2. तरण
  3. वेग
  4. ऊर्जा
    Solutionसमाधान
    Kilowatt-hour (kWh) is a unit of energy, commonly used to measure electrical energy consumption.

    Solving path: kWh = Kilowatt × Hour = Power × Time = Energy. Watt (or Kilowatt) alone is power. The moment you multiply power by time, you get energy. Answer: Energy (ऊर्जा).


    Why this question: The calorie/heat of vaporisation question tests knowledge of the older (pre-SI) heat unit still used in Indian classroom contexts and older exam papers.

    Previous Year Questionपिछले वर्ष का प्रश्न2017
    वाष्प के मापने की इकाई है–
    वाष्प के मापने की इकाई है–
    1. ताप्रक्रम
    2. कैलोरी
    3. इनमें से कोई नहीं
    4. सेंटियरस
      Solutionसमाधान
      Heat of vaporization is measured in Calories (कैलोरी) or Joules, which measure the energy required to convert liquid to vapor.

      Solving path: Vaporisation requires energy input (latent heat). Energy in older / practical contexts is measured in Calories (कैलोरी), which is the non-SI but widely used heat unit (1 cal ≈ 4.18 J). The SI unit would be Joule, but since Joule is not among the options here, Calorie is correct. Answer: Calorie (कैलोरी).


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