§ 1 ✓NCERT Class 11 · Physics · Chapter 1

Chapter test: Units and Measurements

30 questions · Solve each question on paper first, then open "Show answer" to check your working.

QCC Notes · Class 11 Physics NCERT-aligned Updated 26 Sep 2026

Q1 · MCQ · SI UNITS
The SI base unit of luminous intensity is:
1. watt
2. candela
3. lumen
4. lux
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(b) candela — cd measures luminous intensity; watt = power, lumen/lux = flux/illuminance
Q2 · NUMERICAL VALUE · SIGNIFICANT FIGURES
The number of significant figures in 0.00650 is ______.
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3 — leading zeros never count; 6, 5 and the trailing decimal zero do
Q3 · MCQ · DIMENSIONAL ANALYSIS
Which equation is dimensionally correct?
1. v² = u² + 2as
2. v = at²
3. T = 2π√(g/l)
4. s = at
Show answer
(a) — all terms [L²T⁻²]; (b) gives [L], (c) gives [T⁻¹], (d) gives [L T⁻¹]
Q4 · MCQ · DIMENSIONS
Which physical quantity has the same dimensions as impulse?
1. force
2. momentum
3. power
4. energy
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(b) momentum — impulse = FΔt = [M L T⁻¹] = momentum; impulse equals Δp
Q5 · NUMERICAL VALUE · ERRORS
The percentage errors in measuring the mass and volume of a body are 2% and 3%. The percentage error in the calculated density (m/V) is ______ %.
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5 — fractional errors add: 2% + 3%
Q6 · NUMERICAL VALUE · UNIT CONVERSION
A scooter moves at 72 km h⁻¹. Its speed in SI base units is ______ m s⁻¹.
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20 — 72 × 1000/3600 = 20 m s⁻¹
Q7 · MCQ · DIMENSIONAL FORMULAE
The dimensional formula of Planck's constant is:
1. [M L² T⁻²]
2. [M L T⁻¹]
3. [M L² T⁻¹]
4. [M L² T⁻³]
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(c) [M L² T⁻¹] — h = E/ν = [M L² T⁻²]/[T⁻¹]
Q8 · MCQ · SIGNIFICANT FIGURES
The sum 12.11 + 18.0 + 1.012, reported with correct precision, is:
1. 31.122
2. 31.12
3. 31.1
4. 31
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(c) 31.1 — least decimal places = 1 (from 18.0)
Q9 · NUMERICAL VALUE · UNIT CONVERSION
Given 1 J = 10ⁿ erg, the value of n is ______.
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7 — 1 J = 1 kg m² s⁻² → 10³ g × 10⁴ cm² = 10⁷ erg
Q10 · MCQ (DIAGRAM) · LENGTH UNITS

Figure T.1 — Astronomical length ladder

Bar lengths show each unit in metres (log scale); use the read-outs to answer.

1 AU
1.496 × 10¹¹ m

1 light year
9.46 × 10¹⁵ m

1 parsec
3.08 × 10¹⁶ m

From the ladder, 1 parsec equals:
1. 3.26 light years
2. 9.46 light years
3. 3.08 light years
4. 1.496 light years
Show answer
(a) 3.26 ly — 3.08 × 10¹⁶ ÷ 9.46 × 10¹⁵ = 3.26
Q11 · MCQ · ERROR PROPAGATION
If Z = A − B with ΔA = 0.2 cm and ΔB = 0.1 cm, then ΔZ equals:
1. 0.1 cm
2. 0.3 cm
3. 0.2 cm
4. 0.0 cm
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(b) 0.3 cm — absolute errors add even in subtraction
Q12 · MCQ · UNITS IN CONTEXT
The light year is a unit of:
1. time
2. speed
3. distance
4. luminous intensity
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(c) distance — distance light travels in one year — a length
Q13 · NUMERICAL VALUE · SAME DIMENSIONS
Among the pairs {h, angular momentum}, {work, power}, how many pairs have members with identical dimensional formulae? ______
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1 — h and L both [M L² T⁻¹]; work [M L² T⁻²] ≠ power [M L² T⁻³]
Q14 · ASSERTION–REASON · SI UNITS
Assertion (A): The kilogram is an SI base unit even though its name contains a prefix.
Reason (R): Multiples and sub-multiples of mass are written with gram as the root (mg, μg), never as micro-kilogram.
Options: (a) both true, R explains A · (b) both true, R does not explain A · (c) A true, R false · (d) A false, R true
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(a) — kg is the only prefixed base unit; multiples use g — R is the working of A
Q15 · ASSERTION–REASON · ROUNDING
Assertion (A): 2.745 rounded to three significant figures is 2.74.
Reason (R): When the digit to drop is exactly 5 with only zeros (or nothing) after, the last retained digit is made even.
Options: (a) both true, R explains A · (b) both true, R does not explain A · (c) A true, R false · (d) A false, R true
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(a) — round-half-to-even: 4 stays even
Q16 · ASSERTION–REASON · DIMENSIONAL ANALYSIS
Assertion (A): Dimensional analysis alone cannot fix the factor 2π in T = 2π√(l/g).
Reason (R): 2π is a dimensionless constant, invisible to the dimensional method.
Options: (a) both true, R explains A · (b) both true, R does not explain A · (c) A true, R false · (d) A false, R true
Show answer
(a) — pure numbers carry no dimensions
Q17 · NUMERICAL VALUE · LEAST COUNT
A screw gauge has pitch 0.5 mm and 50 divisions on its circular scale. Its least count expressed in micrometres is ______ μm.
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10 — LC = 0.5/50 = 0.01 mm = 10 μm
Q18 · NUMERICAL VALUE · DIMENSIONS
The dimensional formula of the gravitational constant is [Mᵃ L³ T⁻²]. The value of a is ______.
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−1 — G = Fr²/m₁m₂ → [M L T⁻²][L²][M⁻²] = [M⁻¹ L³ T⁻²]
Q19 · NUMERICAL VALUE · PREFIXES
The number of nanometres in exactly 1 millimetre is 10ⁿ. The value of n is ______.
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6 — 1 mm = 10⁻³ m; 1 nm = 10⁻⁹ m → 10⁶ nm
Q20 · MCQ · DIMENSIONAL ANALYSIS
Deriving the wave-speed relation v = k√(F/μ) dimensionally leaves k undetermined because:
1. k has dimensions of speed
2. k is a dimensionless constant, beyond the reach of dimensional analysis
3. F and μ have the same dimensions
4. the wave equation is dimensionally inconsistent
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(b) — dimensionless constants are invisible to dimensional analysis
B1 · NUMERICAL VALUE
The density of a material is 4 g cm⁻³ in the CGS system. In a system where the unit of length is 10 cm and the unit of mass is 100 g (time unchanged), its numerical value is ______.
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4 × 10⁻⁵ — n₂ = n₁(M₁/M₂)¹(L₁/L₂)³ = 4 × (1/100) × (1/10)³ = 4 × 10⁻² × 10⁻³ = 4 × 10⁻⁵ (new units are larger → smaller number)
B2 · MCQ
The dimensional formula of resistivity is:
1. [M L² T⁻³ A⁻²]
2. [M L³ T⁻³ A⁻²]
3. [M L T⁻³ A⁻²]
4. [M L² T⁻³ A⁻¹]
Show answer
(b) [M L³ T⁻³ A⁻²] — ρ = RA/l = [M L² T⁻³ A⁻²][L]/[L²] → [M L³ T⁻³ A⁻²]; option (a) is resistance
B3 · MCQ
Which of the following is NOT an SI base unit?
1. kelvin
2. mole
3. candela
4. radian
Show answer
(d) radian — radian is a supplementary (dimensionless) unit; the other three are base units
B4 · MCQ
If energy E, velocity v and time T are chosen as base quantities, the dimension of mass is:
1. [E v⁻²]
2. [E v²]
3. [E² v⁻²]
4. [E v⁻¹ T⁻¹]
Show answer
(a) [E v⁻²] — m = 2E/v² (from KE = ½mv²) → [M] = [E][v⁻²]; check: [M L² T⁻²]/[L² T⁻²] = [M] ✔
B5 · ASSERTION–REASON
Assertion (A): T = 2π√(l/g) cannot be obtained in full from dimensional analysis alone.
Reason (R): The factor 2π is dimensionless and therefore invisible to the method.
Options: (a) both true, R explains A · (b) both true, R does not explain A · (c) A true, R false · (d) A false, R true
Show answer
(a) — dimensional analysis gives T = k√(l/g); 2π needs the full pendulum differential equation
B6 · MCQ
The dimensional formula of magnetic flux is:
1. [M L² T⁻² A⁻¹]
2. [M T⁻² A⁻¹]
3. [M L² T⁻³ A⁻¹]
4. [M L T⁻² A⁻¹]
Show answer
(a) [M L² T⁻² A⁻¹] — Φ = B·A = [M T⁻² A⁻¹][L²]; option (b) is B itself — the intended trap
B7 · STATEMENT
The value of 5.6 − 0.2, reported with correct precision, is:
1. 5.4
2. 5.40
3. 5.400
4. 5.4000
Show answer
(a) 5.4 — both terms have 1 decimal place → result keeps 1 decimal place; trailing zeros would overclaim precision
B8 · NUMERICAL VALUE
The length 12.65 cm rounded to three significant figures is ______ cm.
Show answer
12.6 — third significant figure: digit after 6 is exactly 5 → round-half-to-even keeps 6 → 12.6 (not 12.7)
B9 · MCQ
1 kilowatt-hour equals:
1. 3.6 × 10³ J
2. 3.6 × 10⁶ J
3. 3.6 × 10⁵ J
4. 1.6 × 10⁻¹⁹ J
Show answer
(b) 3.6 × 10⁶ J — 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
B10 · NUMERICAL VALUE
A length of 10.0 cm is measured with a metre scale of least count 0.1 cm. Taking the uncertainty as one least count, the percentage error in the measurement is ______ %.
Show answer
1 — % error = (0.1/10.0) × 100 = 1% (one least count over the reading)

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Figure T.1 — Astronomical length ladder