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Measurement – Foundation of Science - Introduction: What is Measurement?-advanced

Grade 9CBSE

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

🔑Concepts

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Measurement is the process of comparison of an unknown physical quantity with a known fixed standard quantity of the same nature, called a unit.

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A physical quantity (QQ) is expressed as the product of its numerical value (nn) and its unit (uu): Q=n×uQ = n \times u.

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The numerical value of a physical quantity is inversely proportional to the size of the unit chosen: n∝1un \propto \frac{1}{u}. This implies n1u1=n2u2n_1 u_1 = n_2 u_2.

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Fundamental Quantities are independent physical quantities that cannot be expressed in terms of other quantities (e.g., Mass, Length, Time).

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Derived Quantities are those that are expressed in terms of fundamental quantities (e.g., Velocity, Force, Area).

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The International System of Units (SI) defines seven base units: Meter (mm), Kilogram (kgkg), Second (ss), Kelvin (KK), Ampere (AA), Candela (cdcd), and Mole (molmol).

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Accuracy indicates how close a measurement is to the true or accepted value, while Precision refers to the degree of consistency or reproducibility of the measurements.

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Least Count is the smallest value that can be measured accurately by a measuring instrument.

📐Formulae

Q=n×uQ = n \times u

n1u1=n2u2n_1 u_1 = n_2 u_2

Density=MassVolume=ML3\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{M}{L^3}

Relative Error=Δaamean\text{Relative Error} = \frac{\Delta a}{a_{mean}}

Percentage Error=(Δaamean)×100%\text{Percentage Error} = \left( \frac{\Delta a}{a_{mean}} \right) \times 100\%

💡Examples

Problem 1:

A car is traveling at a speed of 72 km/h72 \text{ km/h}. Convert this speed into SI units (m/s\text{m/s}) using the principle n1u1=n2u2n_1 u_1 = n_2 u_2.

Solution:

Given n1=72n_1 = 72, u1=km/hu_1 = \text{km/h}. We need to find n2n_2 for u2=m/su_2 = \text{m/s}. Since 1 km=1000 m1 \text{ km} = 1000 \text{ m} and 1 hour=3600 s1 \text{ hour} = 3600 \text{ s}: n2=n1×u1u2n_2 = n_1 \times \frac{u_1}{u_2} n2=72×1000 m3600 sn_2 = 72 \times \frac{1000 \text{ m}}{3600 \text{ s}} n2=72×518n_2 = 72 \times \frac{5}{18} n2=4×5=20n_2 = 4 \times 5 = 20 So, the speed is 20 m/s20 \text{ m/s}.

Explanation:

This demonstrates the conversion of units by keeping the physical quantity constant while changing the magnitude and unit system.

Problem 2:

The length of a rod is measured as 2.50 cm2.50 \text{ cm} using a vernier caliper. If the true length is 2.48 cm2.48 \text{ cm}, calculate the percentage error.

Solution:

Absolute Error=∣Measured Value−True Value∣\text{Absolute Error} = |\text{Measured Value} - \text{True Value}| Absolute Error=∣2.50−2.48∣=0.02 cm\text{Absolute Error} = |2.50 - 2.48| = 0.02 \text{ cm} Percentage Error=0.022.48×100%\text{Percentage Error} = \frac{0.02}{2.48} \times 100\% Percentage Error≈0.806%\text{Percentage Error} \approx 0.806\%

Explanation:

Percentage error provides a measure of the accuracy of the measurement relative to the actual size of the object.