Units and Measurements

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A unit is a standard measure of any physical quantity that is internationally accepted for comparison. It provides a reference to express the magnitude of a quantity. Example: When we say the length o…

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1. Length - metre (m) 2. Mass - kilogram (kg) 3. Time - second (s) 4. Temperature - kelvin (K) 5. Electric current - ampere (A) 6. Luminous intensity - candela (cd) 7. Amount of substance - mole (mol)…

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Fundamental quantities do not depend on other quantities for measurement. Examples: length, mass, time. Derived quantities depend on fundamental quantities and can be expressed in terms of them. Exam…

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A dimensional formula expresses a derived quantity in terms of powers of fundamental quantities using square brackets. Velocity = [L¹M⁰T⁻¹] or [LT⁻¹] Acceleration = [L¹M⁰T⁻²] or [LT⁻²]…

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Let T ∝ lᵃ gᵇ, so T = k lᵃ gᵇ Equating dimensions: [T] = [L]ᵃ [LT⁻²]ᵇ [M⁰L⁰T¹] = [Lᵃ⁺ᵇT⁻²ᵇ] Comparing: a + b = 0 and -2b = 1 Solving: b = -1/2, a = 1/2 Therefore: T = k√(l/g) Experimentally, k = 2π…

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Parallax is the apparent change in position of an object due to change in position of observer. For large distances: Two observers at distance b apart observe an object. The parallax angle θ (in radi…

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Work has dimensional formula [L²M¹T⁻²] Let 1 J = x erg 1 [L₁²M₁¹T₁⁻²] = x [L₂²M₂¹T₂⁻²] Substituting SI and CGS units: x = (kg/g) × (m/cm)² × (s/s)⁻² x = (10³/1) × (100/1)² × 1 x = 10³ × 10⁴ = 10⁷ T…

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Accuracy: How close a measurement is to the true/actual value. Precision: How close repeated measurements are to each other (reproducibility). Yes, a measurement can be accurate but not precise - if …