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Units and Measurements – Class 11 Physics notes, important questions and MCQs

NCERT Class 11 Physics, chapter 1. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Physics measures quantities in standard units. The SI system has seven base units; dimensions check equations, and significant figures and errors express precision.

Units and dimensions

SI base units: metre, kilogram, second, ampere, kelvin, mole, candela.
Dimensional formula: force [MLT⁻²], energy [ML²T⁻²], pressure [ML⁻¹T⁻²].
Dimensional analysis checks equations and converts units, but cannot find pure-number constants.

Errors and significant figures

Absolute error, relative error = Δa/a, percentage error = (Δa/a) × 100.
For Z = AᵖBᵠ, ΔZ/Z = pΔA/A + qΔB/B; errors add in sums and differences.
Result of multiplication keeps the least number of significant figures among the inputs.

Key terms

Dimensional formula: expression of a quantity in powers of M, L, T etc.
Significant figures: reliable digits plus the first uncertain digit
Principle of homogeneity: every term in a correct physical equation must have the same dimensions

Formulas

ΔZ/Z = pΔA/A + qΔB/B for Z = AᵖBᵠ

Important questions with answers

Check the correctness of v² = u² + 2as using dimensions.2 marks

[v²] = L²T⁻², [u²] = L²T⁻², [as] = LT⁻² × L = L²T⁻². All terms match, so the equation is dimensionally correct.

Using dimensions, show how the time period of a simple pendulum depends on length l, mass m and g.3 marks

Let T = k lᵃ mᵇ gᶜ. [T] = Lᵃ Mᵇ (LT⁻²)ᶜ. Matching: M: b = 0; L: a + c = 0; T: −2c = 1, so c = −½, a = ½. T = k√(l/g), independent of mass (k = 2π from experiment).

State three limitations of dimensional analysis. The length and breadth of a rectangle are (5.0 ± 0.1) cm and (2.0 ± 0.1) cm. Find its area with the error, and the percentage error.5 marks

Limitations: it cannot find dimensionless constants (like 2π); it cannot derive equations with trigonometric, exponential or log functions or with sums of terms; it cannot tell whether a quantity is scalar or vector. Area = 5.0 × 2.0 = 10 cm². ΔA/A = 0.1/5 + 0.1/2 = 0.02 + 0.05 = 0.07, so ΔA = 0.7 cm². Area = (10 ± 0.7) cm², percentage error 7%.

Quick revision

Seven SI base units.
Dimensions cannot give numerical constants.
Relative errors add in products.

Exam tips

Trailing zeros after a decimal point are significant (2.500 has 4).
When rounding, keep one extra digit during working and round only the final answer to the right significant figures.

Practice MCQs

SI unit of luminous intensity is
1. lumen
2. lux
3. candela
4. watt
Show answer
Answer: (c) candela. Base unit.
Dimensional formula of force is
1. [MLT⁻¹]
2. [ML²T⁻²]
3. [MLT⁻²]
4. [ML⁻¹T⁻²]
Show answer
Answer: (c) [MLT⁻²]. Mass × acceleration.
Number of significant figures in 0.00450 is
1. 2
2. 3
3. 5
4. 6
Show answer
Answer: (b) 3. 4, 5 and trailing 0.
Dimensions of pressure are same as those of
1. force
2. power
3. energy per unit volume
4. momentum
Show answer
Answer: (c) energy per unit volume. [ML⁻¹T⁻²].
The dimensions of (1/2)ρv² are the same as those of
1. force
2. power
3. pressure
4. momentum
Show answer
Answer: (c) pressure. Energy per volume.
If error in radius is 2%, error in volume of a sphere is
1. 2%
2. 4%
3. 6%
4. 8%
Show answer
Answer: (c) 6%. V ∝ r³.
Planck's constant has the same dimensions as
1. angular momentum
2. energy
3. power
4. force
Show answer
Answer: (a) angular momentum. [ML²T⁻¹].
The period of a pendulum T = 2π√(l/g) is measured with 2% error in T and 1% error in l. Error in g is
1. 3%
2. 4%
3. 5%
4. 2%
Show answer
Answer: (c) 5%. g ∝ l/T²: 1 + 2 × 2.

All chapters of Class 11 Physics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.