Skip to content

Chapter 12 · Class 11 Physics

Units and Measurements — Important Questions

34 questions With answers CBSE format

SUMMARY: This chapter focuses on the fundamental concepts of units and measurements, which are essential for scientific experiments and understanding physical quantities.
KEY TOPICS: Physical quantities, SI units, measurement of length, measurement of mass, measurement of time, accuracy and precision, significant figures, dimensional analysis, errors in measurement.

Previous chapter Thermodynamics Next chapter Waves

Multiple Choice Questions (MCQs) 5 questions

Q1 1 Mark

The SI unit of force is:

AJoule

BNewton

CWatt

DPascal

Check answerHide answer

Correct answer: Option 2 — Newton

Q2 1 Mark

Which of the following is a fundamental quantity?

AVelocity

BForce

CMass

DPressure

Check answerHide answer

Correct answer: Option 3 — Mass

Q3 1 Mark

The dimensional formula of pressure is:

A[ML⁻¹T⁻²]

B[MLT⁻²]

C[ML²T⁻²]

D[MT⁻²]

Check answerHide answer

Correct answer: Option 1 — [ML⁻¹T⁻²]

Q4 1 Mark

The number of significant figures in 0.00450 is:

A2

B3

C4

D5

Check answerHide answer

Correct answer: Option 2 — 3

Q5 1 Mark

1 light year equals approximately:

A9.46 × 10⁸ m

B9.46 × 10¹² m

C9.46 × 10¹⁵ m

D9.46 × 10¹⁸ m

Check answerHide answer

Correct answer: Option 3 — 9.46 × 10¹⁵ m

Short Answer Questions 5 questions

Q6 3 Marks

Define fundamental and derived quantities with two examples each.

View sample solutionHide solution

Fundamental quantities cannot be expressed in terms of others. SI has 7: length (m) mass (kg) time (s) electric current (A) thermodynamic temperature (K) amount of substance (mol) and luminous intensity (cd). Derived quantities are combinations of fundamentals: velocity (m/s) force (kg m/s² = N) energy (kg m²/s² = J) etc.

Q7 3 Marks

State the principle of homogeneity of dimensions.

View sample solutionHide solution

Principle of homogeneity: a physical equation is dimensionally correct only if all terms on both sides have the same dimensions. Used to verify equations and to derive relationships among physical quantities. Example: v = u + at — all three terms have dimensions [LT⁻¹] ✓.

Q8 3 Marks

Find the dimensional formula of (a) energy, (b) angular momentum.

View sample solutionHide solution

(a) Energy = force × distance = [MLT⁻²][L] = [ML²T⁻²]. (b) Angular momentum L = mvr → [M][LT⁻¹][L] = [ML²T⁻¹]. Both can be derived from the basic dimensional formulas of mass length and time.

Q9 3 Marks

How many significant figures are in (a) 4.560 × 10⁻³ (b) 0.000450?

View sample solutionHide solution

(a) 4.560 × 10⁻³: leading zeros (none) ignored; 4 5 6 0 are all significant — 4 sig figs. (b) 0.000450: leading zeros (3) not significant; 4 5 0 (the trailing zero after a decimal IS significant) — 3 sig figs.

Q10 3 Marks

Convert 60 km/h to m/s.

View sample solutionHide solution

60 km/h = 60 × 1000 m / 3600 s = 60000/3600 = 16.67 m/s. Useful conversion: divide by 3.6 to convert km/h → m/s; multiply by 3.6 to go m/s → km/h.

Long Answer Questions 6 questions

Q11 6 Marks

Verify dimensionally the equation s = ut + (1/2)at², where s is displacement, u initial velocity, a acceleration, t time.

View sample solutionHide solution

LHS: s = [L]. RHS: ut = [LT⁻¹][T] = [L]; (1/2)at² = [LT⁻²][T²] = [L]. All terms have dimension [L] so the equation is dimensionally homogeneous. Hence the equation is dimensionally correct. (Note: dimensional check confirms correctness only up to a dimensionless constant — it cannot fix the factor 1/2.)

Q12 6 Marks

Using dimensional analysis derive the formula for the time period T of a simple pendulum in terms of its length L, mass m, and acceleration due to gravity g.

View sample solutionHide solution

Assume T = k · L^a · m^b · g^c where k is dimensionless. Dimensions: [T] = [L]^a [M]^b [LT⁻²]^c = [M^b · L^(a+c) · T^(−2c)]. Equating: M: b = 0; L: a + c = 0; T: −2c = 1 ⇒ c = −1/2. Then a = 1/2. So T = k √(L/g). Experimentally k = 2π. Note that mass does not appear — pendulum period is independent of bob mass.

Q13 6 Marks

Calculate the relative error in the volume of a sphere if the error in its radius is 1%.

View sample solutionHide solution

V = (4/3)πr³. Taking ln: ln V = ln(4π/3) + 3 ln r. Differentiating: ΔV/V = 3 (Δr/r). With Δr/r = 1% = 0.01: ΔV/V = 3 × 0.01 = 0.03 = 3%. The relative error in volume is 3 times the relative error in radius (since V ∝ r³). General rule: in z = x^a y^b z^c the relative error is |a|(Δx/x) + |b|(Δy/y) + |c|(Δz/z).

Q14 6 Marks

Discuss the rules for determining significant figures and round 4.567 to 3 significant figures.

View sample solutionHide solution

Rules: (1) Non-zero digits are always significant. (2) Zeros between non-zero digits are significant. (3) Leading zeros are NOT significant. (4) Trailing zeros after a decimal ARE significant; without a decimal they are ambiguous. (5) In scientific notation all digits in the coefficient are significant. Rounding 4.567 to 3 sig figs: look at the 4th digit (7); since 7 ≥ 5 round up the third digit (6 → 7). Result: 4.57.

Q15 6 Marks

Distinguish between accuracy and precision with examples.

View sample solutionHide solution

Accuracy: closeness of a measurement to the true value. Precision: closeness of repeated measurements to each other (reproducibility). Example: true mass = 5.00 g. Measurements (a) 4.95 4.96 4.97 → highly precise (close to each other) but only fairly accurate. (b) 4.50 5.00 5.50 → less precise but average is accurate. Good experiments aim for both. Systematic errors hurt accuracy; random errors hurt precision.

Q16 6 Marks

Differentiate between accuracy and precision in tabular form with one example each.

Assertion–Reason Questions 5 questions

Q17 1 Mark

Assertion (A): Dimensional analysis can verify whether an equation is correct.

Reason (R): Both sides of a physically meaningful equation must have the same dimensions.

Show explanationHide explanation

Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Q18 1 Mark

Assertion (A): Mass length and time are fundamental physical quantities.

Reason (R): They cannot be expressed as combinations of other physical quantities.

Show explanationHide explanation

Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Q19 1 Mark

Assertion (A): Trailing zeros after a decimal point are significant.

Reason (R): They convey the precision of the measurement.

Show explanationHide explanation

Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Q20 1 Mark

Assertion (A): The relative error in volume of a sphere is three times the relative error in its radius.

Reason (R): V = (4/3)πr³ and the exponent of r becomes a multiplier in the error formula.

Show explanationHide explanation

Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Q21 1 Mark

Assertion (A): Dimensional analysis cannot determine the value of dimensionless constants in a formula.

Reason (R): Dimensionless constants like 2π or 1/2 do not affect the dimensions of either side of an equation.

Show explanationHide explanation

Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Statement-Based Questions 5 questions

Q22 1 Mark

Statement 1: The SI system has seven base units.

Statement 2: Other units are derived from these base units.

Show answerHide answer

Correct answer: Option 1 — Both statements are true.

Q23 1 Mark

Statement 1: Force has dimensions [MLT⁻²].

Statement 2: Energy has dimensions [ML²T⁻²].

Show answerHide answer

Correct answer: Option 1 — Both statements are true.

Q24 1 Mark

Statement 1: Systematic errors arise from a fixed cause and bias all readings the same way.

Statement 2: Random errors arise from many small sources and average out over many readings.

Show answerHide answer

Correct answer: Option 1 — Both statements are true.

Q25 1 Mark

Statement 1: A precise measurement need not be accurate.

Statement 2: An accurate measurement need not be precise.

Show answerHide answer

Correct answer: Option 1 — Both statements are true.

Q26 1 Mark

Statement 1: The number of significant figures depends on precision of the measurement.

Statement 2: Leading zeros are not significant but trailing zeros after a decimal are.

Show answerHide answer

Correct answer: Option 1 — Both statements are true.

Case Study / Passage Questions 3 questions

Q27 3 Marks

A student is asked to derive a formula for the time period T of a simple pendulum using dimensional analysis. The student assumes T depends on the length L of the pendulum the mass m of the bob and the acceleration due to gravity g. Without performing any actual experiment the student must use the principle of homogeneity of dimensions to find the dependence.

The correct dimensional dependence is:

AT ∝ L

BT ∝ √L

CT ∝ L²

DT ∝ √(L/g)
Regarding mass m the dimensional analysis shows that:

AMass appears

BMass does not appear

CCannot determine

DDepends on bob shape
Why does mass not appear in the dimensional analysis?

Show answersHide answers

1. Option 4 — T ∝ √(L/g)

2. Option 2 — Mass does not appear

3. Assume T = k · L^a · m^b · g^c. Dimensions: [T] = [L]^a [M]^b [LT⁻²]^c = [M^b L^(a+c) T^(−2c)]. Equating exponents: M: b = 0; L: a + c = 0; T: −2c = 1 ⇒ c = −1/2 ⇒ a = +1/2. Hence T = k √(L/g). Mass disappears (b = 0). Experimentally k = 2π but dimensional analysis cannot fix this dimensionless constant.

Q28 3 Marks

In a physics laboratory a student measures the length of a rod using a metre scale (least count 1 mm) and finds it to be 56.4 cm. Another student uses a vernier calliper (least count 0.01 cm) and obtains 56.42 cm. The teacher asks the class to identify the number of significant figures in each reading and to explain why both are correct.

The number of significant figures in 56.4 cm and 56.42 cm respectively is:

A2 and 3

B3 and 4

C4 and 5

D2 and 4
The reading with higher precision is:

AThe first one

BThe second one

CBoth equal

DCannot decide
Why is the second measurement more precise than the first?

Show answersHide answers

1. Option 2 — 3 and 4

2. Option 2 — The second one

3. 56.4 cm has 3 significant figures (5, 6, 4); 56.42 cm has 4 significant figures (5, 6, 4, 2). The instrument with smaller least count (vernier 0.01 cm vs scale 0.1 cm) gives a measurement with one more significant digit — hence the second is more precise. Both are correct readings; precision is limited by the instrument used.

Q29 3 Marks

A satellite orbiting Earth has its data given in mixed units: orbital radius = 7000 km altitude above surface = 600 km speed = 27000 km/h period = 100 min. To use the Newton's law of gravitation in SI units the engineer needs to convert all the values. R_E = 6400 km.

The orbital radius in SI units (m) equals:

A7000 km

B7 × 10³ m

C7 × 10⁶ m

D7 × 10⁹ m
27000 km/h in m/s equals:

A7.5 m/s

B75 m/s

C750 m/s

D7500 m/s
Convert the orbital period 100 min to SI seconds.

Show answersHide answers

1. Option 3 — 7 × 10⁶ m

2. Option 4 — 7500 m/s

3. 7000 km = 7000 × 1000 m = 7 × 10⁶ m. Speed: 27000 km/h × (1000 m/km)/(3600 s/h) = 7500 m/s. Period: 100 min × 60 s/min = 6000 s. Conversion to SI is essential before using physical formulas because constants like G are quoted in SI (G = 6.67 × 10⁻¹¹ N·m²/kg²). Mixing units leads to incorrect results.

Table-Based Questions 4 questions

Q30 3 Marks

Study the SI base units and answer:

Quantity	SI Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Thermodynamic temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

The number of SI base units is:

A5

B6

C7

D8
Which of the following is an SI base unit (not derived)?

ACoulomb

BPascal

CNewton

DAmpere
Express the unit newton in terms of SI base units.

Show answersHide answers

1. Option 3 — 7

2. Option 4 — Ampere

3. SI has 7 base units corresponding to 7 fundamental quantities — none can be expressed in terms of others. Derived units (newton coulomb pascal joule etc.) are products/quotients of base units. For instance 1 N = 1 kg·m/s² (combines kg m and s).

Q31 3 Marks

Study the dimensional formulas:

Quantity	Dimensional formula
Velocity	[LT⁻¹]
Acceleration	[LT⁻²]
Force	[MLT⁻²]
Pressure	[ML⁻¹T⁻²]
Energy	[ML²T⁻²]
Power	[ML²T⁻³]
Angular momentum	[ML²T⁻¹]

The dimensional formula of energy is:

A[ML⁻¹T⁻²]

B[MLT⁻²]

C[ML²T⁻²]

D[ML²T⁻¹]
Which quantity has dimensional formula [ML⁻¹T⁻²]?

AVelocity

BAcceleration

CPressure

DPower
Why is dimensional analysis useful in physics?

Show answersHide answers

1. Option 3 — [ML²T⁻²]

2. Option 3 — Pressure

3. Dimensional formulas show how a quantity depends on the fundamental dimensions M L T (and others when needed). They are useful to verify equations check unit conversions and derive relationships through dimensional analysis. Two quantities with the same dimensions can be added/equated; quantities with different dimensions cannot.

Q32 6 Marks

Use dimensional analysis to derive the formula for the time period T of a simple pendulum in terms of length L, mass m, and g.

Quantity	Symbol	Dimension
Time period	T	[T]
Length	L	[L]
Mass	m	[M]
Acceleration due to gravity	g	[LT⁻²]

Q33 6 Marks

Compute the relative error in the volume of a sphere if the error in radius is 1.5%, and the percentage error in surface area for the same Δr/r.

Quantity	Formula	Relation to r
Volume V	(4/3)πr³	V ∝ r³
Surface area S	4πr²	S ∝ r²
Δr/r	1.5%	Given

Picture-Based Questions 1 question

Q34 3 Marks

Study the vernier caliper diagram and answer:

Units and Measurements figure

The least count of this vernier caliper is:

A0.001 cm

B0.01 cm

C0.1 cm

D1 cm
The reading shown by the vernier caliper is:

A2.04 cm

B2.34 cm

C2.40 cm

D2.44 cm
Explain how the vernier scale increases the precision of measurement.

Show answersHide answers

1. Option 2 — 0.01 cm

2. Option 2 — 2.34 cm

3. Least count = (1 main scale division)/(no. of vernier scale divisions) = 1 mm / 10 = 0.1 mm = 0.01 cm. Vernier reading = main scale value just before zero of vernier (2.3 cm) + (matching division × least count) = 2.3 + 4 × 0.01 = 2.34 cm. The vernier increases precision tenfold over the main scale.

Previous chapter Thermodynamics Next chapter Waves

Make a full Physics paper on Units and Measurements.

Pick the question mix, set the marks, hit generate. You get a ready-to-print paper with an answer key.

Generate your paper — free