How many fundamental quantities are there in the SI system?

There are 7 fundamental (base) quantities in the SI system: length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), luminous intensity (candela), and amount of substance (mole). All other physical quantities are derived from these.

What is the dimensional formula of gravitational constant G?

From Newton's law of gravitation F = Gm₁m₂/r², we get G = Fr²/m₁m₂. Substituting dimensions: G = [M¹L¹T⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. So the dimensional formula of G is [M⁻¹ L³ T⁻²].

What are the limitations of dimensional analysis?

Dimensional analysis cannot: (1) determine dimensionless constants like 2π; (2) be used for equations involving trigonometric, exponential, or logarithmic functions; (3) distinguish between scalar and vector quantities; (4) derive complete physical laws independently.

SI Units and Dimensional Analysis

Units and Measurements • Class 11 Physics • NCERT • CBSE

The SI system has 7 fundamental units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), candela (luminous intensity), and mole (amount of substance). Dimensional analysis checks the correctness of equations and derives unknown relations.

Key Formulas

[Force] = M¹ L¹ T⁻²
[Energy] = M¹ L² T⁻²
[Power] = M¹ L² T⁻³
T = 2π√(l/g) [derived by dimensional analysis]

Frequently Asked Questions

How many fundamental quantities are there in the SI system?: There are 7 fundamental (base) quantities in the SI system: length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), luminous intensity (candela), and amount of substance (mole). All other physical quantities are derived from these.
What is the dimensional formula of gravitational constant G?: From Newton's law of gravitation F = Gm₁m₂/r², we get G = Fr²/m₁m₂. Substituting dimensions: G = [M¹L¹T⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. So the dimensional formula of G is [M⁻¹ L³ T⁻²].
What are the limitations of dimensional analysis?: Dimensional analysis cannot: (1) determine dimensionless constants like 2π; (2) be used for equations involving trigonometric, exponential, or logarithmic functions; (3) distinguish between scalar and vector quantities; (4) derive complete physical laws independently.

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