Units, Dimensions and Measurement
Every numerical question in this section of the paper ends with a unit, and a large share of wrong answers come from the unit rather than the physics. A candidate who computes a correct speed in km/h when the options are in m/s, or who converts square metres to square centimetres by multiplying by 100, loses the mark as surely as one who did not know the formula. This chapter therefore does two jobs. It first sets out, from the official notifications, where the Basic Science and Engineering block sits in the RRB papers and how negative marking changes your attempt strategy. It then builds the measurement toolkit the rest of the book relies on: SI units and prefixes, conversions between unit systems, dimensional checking, error handling, and the workshop instruments — the vernier caliper and the micrometer — that an ITI-qualified Assistant Loco Pilot is expected to read without hesitation.
KarmSakha preparation topics covered
- Where Basic Science and Engineering sits in RRB ALP CBT-2 Part A and in the Technician Grade I Signal CBT, read from CEN 01/2025 and CEN 02/2025
- Physical quantities, the seven SI base units, derived units with special names and the rules for writing unit symbols
- FPS, CGS, MKS and SI systems, exact conversion factors and the chain method for converting compound units
- SI prefixes, powers of ten and the area and volume conversion trap
- Dimensional formulas, the principle of homogeneity, and what dimensional analysis can and cannot do
- Accuracy, precision, types of error, percentage error in products and quotients, and significant figures
- Steel rule, vernier caliper and outside micrometer: least count, reading, zero error and its correction
Where Basic Science and Engineering Sits in the RRB Papers
The Assistant Loco Pilot recruitment under Centralised Employment Notice (CEN) 01/2025 runs in stages: a first-stage computer based test (CBT-1) used only for screening, a second-stage CBT (CBT-2), a computer based aptitude test (CBAT), document verification and a medical examination. CBT-2 is split into two parts. Part A carries 100 questions in 90 minutes; Part B carries 75 questions in 60 minutes and tests the trade syllabus prescribed by the Directorate General of Training. The notification states that only Part A marks are counted for shortlisting, provided the candidate secures the qualifying 35 percent in Part B, and that the final ALP panel is prepared on the marks in CBT-2 and CBAT. Section 12.3 then spells out the weighting: candidates must secure a minimum T-score of 42 in each CBAT test battery to qualify, and the merit list gives 70 percent weightage to the marks in Part A of CBT-2 and 30 percent to the CBAT score. That makes Part A the merit-deciding paper, and this book covers one of its three blocks.
The notification lists Part A in three blocks: Mathematics, General Intelligence and Reasoning, and Basic Science and Engineering. For the third block it names the broad topics as Engineering Drawing (projections, views, drawing instruments, lines, geometric figures, symbolic representation), Units, Measurements, Mass Weight and Density, Work Power and Energy, Speed and Velocity, Heat and Temperature, Basic Electricity, Levers and Simple Machines, Occupational Safety and Health, Environment Education and IT Literacy, followed by the word etc. The notification does not publish a subject-wise split of the 100 questions for Part A, so any fixed number you see quoted for this block is an estimate, not an official figure. Treat every listed topic as examinable.
The same block reappears for Technicians. In CEN 02/2025, the CBT for Technician Grade I Signal (Pay Level 5) has a section titled Basic Science and Engineering, shown in the notification's tentative break-up as 35 of 100 questions, with the explicit caution that the distribution is merely indicative. Its list starts with the same physics fundamentals as the ALP list — units, measurements, mass, weight, density, work, power, energy, speed, velocity, heat and temperature — and then goes deeper into electricity and magnetism: electric field and potential, Ohm's law and its limitations, specific resistance, Ampere's law, magnetic force on moving charges and conductors, electromagnetic induction and Faraday's law. Chapters 7 and 8 of this book are written to cover that extension. The Technician Grade III CBT, by contrast, has a General Science section at Class 10 level rather than this block.
Both notifications specify negative marking at one-third of a mark for each wrong answer, and that single rule should shape how you attempt this section. With four options and a one-third penalty, a blind guess has an expected value of exactly zero: one chance in four of gaining 1 mark, three chances in four of losing one-third of a mark, and (1/4)(1) − (3/4)(1/3) = 0. Blind guessing therefore neither helps nor hurts on average, but it adds risk. The moment you can eliminate even one option with certainty, the expectation turns positive: with three options left it becomes (1/3)(1) − (2/3)(1/3) = 1/9 of a mark per guess. More generally, if p is the penalty for a wrong answer as a fraction of a mark (p = 1/3 in both notifications), an accuracy a on the questions you attempt earns a − (1 − a)p per question, which is positive only when a exceeds p/(1 + p). The break-even accuracy is therefore p/(1 + p) = (1/3)/(4/3) = 25 percent.
The practical message is that this block rewards clean recall of definitions and units, and fast, careful arithmetic. Many questions are one-step: identify the SI unit of pressure, pick the correct projection arrangement, choose the extinguisher for an oil fire. Others are two- or three-step numericals of the ITI Workshop Calculation and Science type. The one-step questions are where marks are banked quickly; the numericals are where unit discipline decides whether the arithmetic you did is rewarded. Everything else in this chapter is about making units automatic.
| Paper (notification) | Size and time | Negative marking | Where this book's content is tested |
|---|---|---|---|
| ALP CBT-1 (CEN 01/2025) | 75 questions, 60 minutes | 1/3 mark per wrong answer | General Science at Class 10 level overlaps chapters 2-8; screening only |
| ALP CBT-2 Part A (CEN 01/2025) | 100 questions, 90 minutes | 1/3 mark per wrong answer | Basic Science and Engineering block — all twelve chapters; no official split published |
| ALP CBT-2 Part B (CEN 01/2025) | 75 questions, 60 minutes | 1/3 mark per wrong answer | Trade syllabus (DGT); qualifying 35 percent only |
| Technician Grade I Signal CBT (CEN 02/2025) | 100 questions, 90 minutes | 1/3 mark per wrong answer | Basic Science and Engineering, 35 questions (indicative); chapters 1-8 and 12 |
Physical Quantities and the Seven SI Base Units
A physical quantity is anything that can be measured and expressed as a number multiplied by a unit: length 2.5 m, mass 40 kg, time 12 s. The number alone means nothing — 2.5 could be metres, feet or kilometres — so in every answer the unit is part of the value. Quantities are divided into base (fundamental) quantities, which are chosen as independent of each other, and derived quantities, which are built from the base quantities by multiplication and division. Speed is derived from length and time, force from mass, length and time, and so on.
The International System of Units (SI) has seven base units, listed in the table below. Since the redefinition that took effect on 20 May 2019, all seven are defined by fixing the numerical values of physical constants — the kilogram, for example, is now defined through the Planck constant rather than through a metal cylinder kept in France. For this exam you do not need the definitions in detail, but you must know the seven quantities, their unit names and their symbols, because questions of the type 'which of these is not a base unit' are common. The usual trap options are the newton, the joule, the volt and the degree Celsius, none of which is a base unit; the kelvin is the base unit of temperature.
Two quantities often confuse candidates. The unit of plane angle, the radian, and the unit of solid angle, the steradian, were once called supplementary units; in the present SI they are treated as dimensionless derived units. Electric current, not electric charge, is the base electrical quantity: the ampere is a base unit, and the coulomb is derived as one ampere-second. Similarly, amount of substance (the mole) is a base quantity even though it looks like a count, and luminous intensity (the candela) completes the list.
Symbols follow fixed rules that the exam occasionally tests directly. A unit symbol is written in lower case unless the unit is named after a person, in which case the first letter is capital: m, kg, s, but N (Newton), Pa (Pascal), W (Watt), K (Kelvin). The full name is always written in lower case, even when it honours a person — newton, pascal, watt — with one exception: in degree Celsius, Celsius keeps its capital letter. Symbols take no plural and no full stop: write 5 kg, not 5 kgs, and not 5 kg. with a full stop in the middle of a sentence. A space separates the number from the symbol, and the kelvin is written without a degree sign — 300 K, not 300 °K. The litre is the one common exception to the case rule, and both l and L are accepted, with L preferred to avoid confusion with the digit 1.
| Base quantity | SI unit | Symbol | Common trap |
|---|---|---|---|
| Length | metre | m | The kilometre and centimetre are multiples, not separate base units |
| Mass | kilogram | kg | The only base unit with a prefix in its name; the gram is not the base unit |
| Time | second | s | Minute and hour are accepted for use with SI but are not SI units |
| Electric current | ampere | A | Charge (coulomb) and voltage (volt) are derived |
| Thermodynamic temperature | kelvin | K | Degree Celsius is a derived unit; kelvin takes no degree sign |
| Amount of substance | mole | mol | Not a unit of mass |
| Luminous intensity | candela | cd | Lumen and lux are derived units |
Derived Units with Special Names
A derived unit is built by applying the defining equation of the quantity to the base units. Velocity is displacement divided by time, so its unit is m/s. Acceleration is change of velocity divided by time, so m/s². Force is mass multiplied by acceleration, so kg m/s², and because this combination is used constantly it has a special name, the newton. The method matters more than memorising the table: if you remember the defining equation of a quantity, you can always rebuild its unit, and that is exactly how questions of the form 'one joule is equal to' are answered.
Work is force multiplied by distance, so one joule is one newton-metre, which expands to kg m²/s². Power is work divided by time, so one watt is one joule per second. Pressure is force divided by area, so one pascal is one newton per square metre. Frequency is the number of cycles per second, so one hertz is one per second. In electricity, one coulomb is one ampere-second, one volt is one joule per coulomb (equivalently one watt per ampere), and one ohm is one volt per ampere. These relations are used again and again in chapters 4, 7 and 8, so it is worth writing them out once in your own notebook in base-unit form.
A frequent trap concerns the newton-metre. Both work (energy) and torque (moment of a force) are expressed as force multiplied by a length, so both have the base-unit form kg m²/s². For energy the SI name is the joule, but torque is conventionally written in N m and is not called joules, because torque is not energy — the length in torque is a perpendicular lever arm, not a distance moved. When an option lists 'joule' as the unit of torque, it is usually meant to be rejected, even though the dimensions match.
Some familiar units are not SI but remain in everyday engineering use in India: the kilowatt-hour for electrical energy billing, the bar for pressure, the litre for volume, the horsepower for engine ratings, and the calorie in older heat problems. You should be able to convert each to its SI equivalent — 1 kWh = 3.6 × 10⁶ J, 1 bar = 10⁵ Pa, 1 L = 10⁻³ m³, 1 metric horsepower = 735.5 W while the British horsepower is about 746 W (745.7 W), and 1 cal = 4.186 J — because questions often give data in these units and options in SI units, or the other way round.
