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Playbook

Units, Measurement and Dimensions

14 q · 7% HARD. SI vs CGS unit recall, dimensional formulas (G, h, force, pressure), 'which is dimensionless?', precision/least-count. Mostly EASY; one HARD per paper at most.

questions in the bank
14
tagged HARD
7%
subtopic(s)
1
worked examples
2

When you’ll see it

A 'find the dimensional formula of X', a unit-conversion (1 dyne = ? N), a 'which is dimensionless?', a match-list of quantity↔unit, or a precision/least-count question.

How this chapter is tested

14 q across 10 years, all under one subtopic (Units and Dimensions). The chapter sets up everything else — dimensional analysis catches algebra errors, and unit conversions appear inside other chapters' calculations too.

Memorise 6 dimensional formulas: Force M·L·T⁻², Energy M·L²·T⁻², Pressure M·L⁻¹·T⁻², Power M·L²·T⁻³, Planck's constant M·L²·T⁻¹ (same as angular momentum), G M⁻¹·L³·T⁻². Anything else can be reconstructed from F=ma or E=½mv² in 30 seconds.

Dimensionless quantities: angle (rad), refractive index, dielectric constant, specific gravity, strain, coefficients of friction, Reynolds number. They're all ratios of like-with-like.

The sub-skills

The rules and habits that decide whether you get a question right.

  • Dimensional formula derivation

    Start from F = ma or E = ½mv², derive everything else. Force = [M·L·T⁻²]. Energy = [M·L²·T⁻²]. Pressure = Force/Area = [M·L⁻¹·T⁻²].

  • CGS ↔ SI conversion

    1 dyne = 10⁻⁵ N (g·cm·s⁻² vs kg·m·s⁻²). 1 erg = 10⁻⁷ J. 1 poise = 0.1 Pa·s. Build conversions from the unit definitions.

  • Dimensionless detection

    If the quantity is a RATIO of two same-dimension things, it's dimensionless. Angle = arc/radius. Refractive index = c/v_medium. Strain = Δl/l.

  • Least count / precision

    Least count = smallest measurable unit (1 mm on a metre scale, 0.01 mm on a vernier). Precision relates to least count; accuracy relates to systematic error. Don't conflate.

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Units, Measurement and DimensionsMODERATE
What is the dimension of gravitational constant?

[Q68 · Apr · 2022]

Example 2Units, Measurement and DimensionsMODERATE
1 dyne (a unit of force in CGS system) equals to

[Q113 · Apr · 2019]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • L⁻¹ vs L

    Pressure is M·L⁻¹·T⁻² (force per AREA — area is L², so dividing gives L⁻¹ in the L-tally). Energy density is also M·L⁻¹·T⁻². If you write +1 instead of −1 you've inverted the answer.

  • Confusing precision and accuracy

    Precision = consistency / least count. Accuracy = closeness to true value. A precise-but-inaccurate measurement clusters around a wrong value. NDA tests precision more than accuracy.

Drill every units, measurement and dimensions question

14 questions from the bank, scoped to the named subtopic.

Drill the 14 questions

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