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Units and Measurements - The International System of Units

Grade 11CBSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The International System of Units (SI) is a modernized metric system based on seven base units and two supplementary units.

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The seven base quantities and their units are: Length (meter, mm), Mass (kilogram, kgkg), Time (second, ss), Electric Current (ampere, AA), Thermodynamic Temperature (kelvin, KK), Amount of Substance (mole, molmol), and Luminous Intensity (candela, cdcd).

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Supplementary units include the Plane Angle (dθd\theta), measured in radians (radrad), and the Solid Angle (dΩd\Omega), measured in steradians (srsr).

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Derived units are units of measurement derived from the seven base units. For example, the unit of Force is the Newton (NN), where 1 N=1 kg⋅m⋅s−21\,N = 1\,kg \cdot m \cdot s^{-2}.

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Physical quantities are expressed as Q=nuQ = nu, where nn is the numerical value and uu is the unit. For a constant quantity, n1u1=n2u2n_1u_1 = n_2u_2.

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Prefixes are used to indicate multiples and sub-multiples of units, such as micro (10−610^{-6}), nano (10−910^{-9}), mega (10610^{6}), and giga (10910^{9}).

📐Formulae

Q=n×uQ = n \times u

n1u1=n2u2n_1 u_1 = n_2 u_2

θ (in radians)=arc length (s)radius (r)\theta \text{ (in radians)} = \frac{\text{arc length (s)}}{\text{radius (r)}}

Ω (in steradians)=Area (A)r2\Omega \text{ (in steradians)} = \frac{\text{Area (A)}}{r^2}

1 rad=180∘π1\text{ rad} = \frac{180^\circ}{\pi}

💡Examples

Problem 1:

Convert a density of 13.6 g/cm313.6\,g/cm^3 into the SI unit (kg/m3kg/m^3).

Solution:

Given n1=13.6n_1 = 13.6, u1=g/cm3u_1 = g/cm^3. We know 1 g=10−3 kg1\,g = 10^{-3}\,kg and 1 cm=10−2 m1\,cm = 10^{-2}\,m. Therefore, 1 cm3=(10−2 m)3=10−6 m31\,cm^3 = (10^{-2}\,m)^3 = 10^{-6}\,m^3. Substituting these values: n2=n1×u1u2=13.6×10−3 kg10−6 m3=13.6×103 kg/m3=13600 kg/m3n_2 = n_1 \times \frac{u_1}{u_2} = 13.6 \times \frac{10^{-3}\,kg}{10^{-6}\,m^3} = 13.6 \times 10^3\,kg/m^3 = 13600\,kg/m^3.

Explanation:

To convert units, we express the old unit in terms of the new unit using the relation n1u1=n2u2n_1u_1 = n_2u_2 and substitute the conversion factors for mass and length.

Problem 2:

Calculate the angle subtended at the center of a circle of radius 2.0 m2.0\,m by an arc of length 50 cm50\,cm.

Solution:

Radius r=2.0 mr = 2.0\,m, Arc length s=50 cm=0.5 ms = 50\,cm = 0.5\,m. The plane angle in radians is given by: θ=sr=0.5 m2.0 m=0.25 rad\theta = \frac{s}{r} = \frac{0.5\,m}{2.0\,m} = 0.25\,rad.

Explanation:

The formula for a plane angle is the ratio of arc length to radius. Ensure both measurements are in the same units (meters) before calculation.