CBSE Class 9 Physics Units and Measurements Notes Set 14

Physical Quantities and Units

Physics is a science of measurement. A physical quantity is expressed as a number followed by a unit: (physical quantity) = (number) x (unit).
1. Fundamental quantities are obtained by the most basic measurements. In mechanics they are mass, length and time; others are temperature, amount of substance, electric current and luminous intensity.
2. Derived quantities are combinations of the fundamental ones, for example force, density, work and pressure.
3. Heat is energy, not a fundamental quantity.

Systems of Units

1. Older systems were the British (FPS: foot, pound, second) and the metric systems (CGS: centimetre, gram, second; MKS: metre, kilogram, second).
2. The International System (SI) is the single system used in all branches of physics. Besides mass, length and time it includes kelvin, mole, ampere and candela as base units, so it is not based on mass, length and time alone.
3. Supplementary units are the radian (plane angle, 2 pi rad = 360°, 1 rad = 57.3°) and the steradian (solid angle).

Base SI Units

Prefixes

Among the prefixes listed the largest is exa (10¹⁸), followed by peta, tera and giga.
Example: the radius of a sodium atom is 1.57 x 10⁻¹⁰ m. Since 1 pm = 10⁻¹² m, it is 1.57 x 10⁻¹⁰ / 10⁻¹² = 157 pm.

Derived Units

A derived unit is obtained by multiplying or dividing base units.
1. Area: m². Volume: m³. Density: kg/m³ (kg m⁻³). Speed and velocity: m/s. Acceleration: m/s².
2. Momentum: kg m/s. Force and weight: newton (N = kg m/s²). Work and energy: joule (J). Power: watt (W). Pressure: pascal (Pa).
3. Units such as N/kg are those of acceleration (force per unit mass).

Uncertainty in Measurement

1. The last digit of a reported measurement is uncertain by one unit of that digit; a length of 1.4 cm means 1.4 +/- 0.1 cm and a time of 5.354 s means 5.354 +/- 0.001 s.
2. Percentage uncertainty = (uncertainty / measured value) x 100. For 3.56 +/- 0.02 g it is \( \dfrac{0.02}{3.56} \times 100 = 0.56\% \approx 0.6\% \).
3. The least count of an instrument is the smallest division on its scale. Measuring about 50 cm with a metre stick of 1 mm divisions gives a percentage error of \( \dfrac{0.1}{50} \times 100 = 0.2\% \).

Standards of Measurement

1. International standards are kept by the International Bureau of Weights and Measures near Paris. In India the national standards are maintained by the National Physical Laboratory, New Delhi, which compares them periodically with the international ones.
2. The metre is now defined as the distance travelled by light in vacuum in 1/299 792 458 second; the second is defined using the radiation of the caesium-133 atom.
3. Ancient Indian length units began with the smallest, the parmanu, and extended to the yojana (about 10 km today). Later units included the gaz and, in the British period, the inch, foot and yard (12 inches = 1 foot, 3 feet = 1 yard, about 0.9 m).