Units and Measurements
➢ Physical Quantity
- The quantities that can be measured by an instrument and by which we can describe physics laws are called physical quantities.
Types of Physical Quantities
- Although the number of physical quantities we measure is very large, we need only a limited number of units to express all the physical quantities since they are interrelated.
- So, certain physical quantities have been chosen arbitrarily, and their units are used for expressing all the physical quantities, such quantities are known as Fundamental, Absolute, or Base Quantities (such as length, time and mass in mechanics)
- All other quantities may be expressed in terms of fundamental quantities.
- They are independent of each other and cannot be obtained from one another.
- An international body named General Conference on Weights and Measures chose seven physical quantities as fundamental:
- In mechanics, we treat length, mass, and time as the three basic or fundamental quantities.
Question 1:The base quantity among the following is
There are seven base quantities,
(v) Amount of substance
(vi) Luminous intensity
- Physical quantities that can be expressed as a combination of base quantities are called derived quantities.
Example: Speed, velocity, acceleration, force, momentum, pressure, energy, etc.
- Besides the seven fundamental physical quantities, two supplementary quantities are also defined, they are:
(i) Plane angle(ii) Solid angle
- Magnitude of physical quantity = (numerical value) x (unit)
The magnitude of a physical quantity is always constant. It is independent of the type of unit.
Example: The length of a metal rod bar is unchanged whether it is measured as 2 meters or 200 cm. Observe the change in the Numerical value (from 2 to 200) as a unit is changed from meter to cm.
- Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic reference standard called unit.
- The units for the fundamental or base quantities are called fundamental or base unit. Other physical quantities are expressed as a combination of these base units and hence, called Derived units.
- A complete set of units, both fundamental and derived, is called a system of units.
➢ Principle Systems of Unit
- There are various system in use over the world: CGS, FPS, SI (MKS), etc.
- Table: Units of some physical quantities in different systems.
➢ Supplementary Units
- Plane angle: radian (rad)
- Solid angle: steradian (sr)
- The SI system is at present, widely used throughout the world.
➢ Definitions of Some Important S.I. Units
- Metre: 1 m = 1,650, 763.73 wavelengths in vaccum, of radiation corresponding to organ-red light of krypton-86.
- Second: 1 s = 9,192, 631,770 time periods of a particular from Ceasium - 133 atom.
- Kilogram: 1 kg = mass of a 1-litre volume of water at 4°C.
- Ampere: It is the current which when flows through two infinitely long straight conductors of negligible cross-section placed at a distance of one meter in a vacuum produces a force of 2 × 10-7 N/m between them.
- Kelvin: 1 K = 1/273.16 part of the thermodynamic temperature of the triple point of water.
- Mole: It is the amount of substance of a system that contains as many elementary particles (atoms, molecules, ions, etc.) as there are atoms in 12 g of carbon - 12.
- Candela: It is luminous intensity in a perpendicular direction of a surface of (1/600000)m2 of a black body at the temperature of the freezing point under a pressure of 1.013 × 105 N/m2.
- Radian: It is the plane angle between two radii of a circle which cut-off on the circumference, an arc equal in length to the radius.
- Steradian: The steradian is the solid angle which having its vertex at the centre of the sphere, cut-off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.
- The magnitudes of physical quantities vary over a wide range. The CGPM recommended standard prefixes for magnitude too large or too small to be expressed more compactly for a certain power of 10.
➢ General Guidelines for using Symbols for SI Units, Some other Units, and SI prefixes
- Symbols for units of physical quantities are printed/written in Roman (upright type), and not in italics.
Example: 1 N is correct, but 1 N is incorrect.
- Unit is never written with capital initial letter even if it is named after a scientist.
Example: SI unit of force is newton (correct) Newton (incorrect)
- For a unit named after a scientist, the symbol is a capital letter. But for other units, the symbol is NOT a capital letter.
Force → newton (N)
Energy → joule (J)
Electric current → ampere (A)
Temperature → kelvin (K)
Frequency → hertz (Hz)
Length → meter (m)
Mass → kilogram (kg)
Luminous intensity → candela (cd)
Time → second (s)
Note: The single exception is L, for the unit litre.
Question 2:Which of the following is a unit that of force?
Nm → Unit of torque
mN → Milli newton → 10–3 N
nm → Nano metre
Ns → Unit of momentum
- Symbols for units do not contain any final full stop at the end of the recommended letter and remain unaltered in the plural, using only the singular form of the unit.
- Use of slash (/) is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one slash is used.
- Prefix symbols are printed in roman (upright) type without spacing between the prefix symbol and the unit symbol. Thus certain approved prefixes written very close to the unit symbol are used to indicate decimal fractions or multiples of a SI unit when it is inconveniently small or large.
- The unit 'fermi', equal to a femtometre or 10-15 m has been used as the convenient length unit in nuclear studies.
- When a prefix is placed before the symbol of a unit, the combination of prefix and symbol is considered as a new symbol, for the unit, which can be raised to a positive or negative power without using brackets. These can be combined with other unit symbols to form a compound unit.
- A prefix is never used alone. It is always attached to a unit symbol and written or fixed before the unit symbol.
► 103/m3 = 1000/m3 or 1000 m-3, but not k/m3 or k m-3.
- Prefix symbol is written very close to the unit symbol without spacing between them, while unit symbols are written separately with spacing with units are multiplied together.
- The use of double prefixes is avoided when single prefixes are available.
- The use of a combination of units and the symbols for the unit is avoided when the physical quantity is expressed by combining two or more units.
➢ Characteristics of Base Units or Standards
- Well defined
- Convenience in use
➢ Some Special Types of Units
- Micron (1μ) = 10-4 cm = 10-6 m (length)
- Angstrom (1 Å) = 10-8 cm = 10-10m (length)
- Fermi (1 f) = 10-13 cm = 10-15 m (length)
- Inch = 2.54 cm (length)
- Mile = 5280 feet = 1.609 km (length)
- Atmosphere = 105 N/m2 = 76 torr = 76 mm of Hg pressure (pressure)
- Litre = 10-3 m3 = 1000 cm3 (volume)
- Carat = 0.0002 kg (weight)
- Pound (Ib) = 0.4536 kg (weight)
Question 3:One astronomical unit is a distance equal to
One astronomical unit is the average distance between earth and sun
1 astronomical Unit (AU) = 1.496 × 1011 m
Accuracy and Precision
- The closeness of a measured value to the actual value of the object being measured is called the accuracy of a substance. For instance, if you obtain a weight measurement of 3.2 kg for a given substance in the lab, but the actual or known weight is 10 kg, then your measurement is not accurate.
- The closeness of two or more measurements to each other is known as the precision of a substance. From the above-given example, we can figure out that, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise.
- Precision is independent of accuracy. The below example will tell you about how you can be precise but not accurate and vice versa.
Question 4:The most precise reading of the mass of an object, among the following is
A measurement having more number of decimal places is the one with the most precision. So, 20.01 g is most precise.
Precision is sometimes separated into:
- Repeatability: The variation arising when the conditions are kept identical, and repeated measurements are taken during a short time period.
- Reproducibility: The variation arising using the same measurement process among different instruments and operators, and over longer time periods.
In other words, accuracy is the degree of closeness between a measurement and the measurement’s true value.
- Precision is the degree to which repeated measurements under the same conditions are unchanged.
- A good analogy for understanding accuracy and precision is to imagine a football player shooting at the goal. If the player shoots into the goal, he is said to be accurate. A football player who keeps striking the same goalpost is precise but not accurate.
- Therefore a football player can be accurate without being precise if he hits the ball all over the place but still scores. A precise player will hit the ball to the same spot repeatedly, irrespective of whether he scores or not.
- A precise and accurate football player will aim at a single spot and score a goal.
Question 5:Which of the following is the most precise measurement?
3 × 10–3
3.0 × 10–3
3.0 × 10–3
3.00 × 10–3
So, fourth measurement is most precise.