Measurement and Experimentation PDF

Term 2 Chapter 1 - MEASUREMENT AND EXPERIMENTATION Systems of Units and Units in S.I. System: Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature. Unit is the quantity of a constant magnitude which is used to measure the magnitu...

Term 2 Chapter 1 - MEASUREMENT AND EXPERIMENTATION Systems of Units and Units in S.I. System: Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature. Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature. Measurement of any physical quantity is meaningless unless its unit is defined. i.e. Physical quantity = (magnitude) × (unit) Choice of Unit: 1. For any measurement, the unit should be of convenient size. 2. There should not be any ambiguity to define the unit. 3. The value of a unit should not change with space and time. Kinds of units: (i) Fundamental units (Basic Units) (ii) Derived Units (i) Fundamental Units: A fundamental unit is that which is independent of any other unit or which can neither be changed nor can be related to any other fundamental unit. The above mentioned units cannot be obtained from any other units. e.g. kilogram, metre, second- units of fundamental quantities - mass, length, time. (ii) Derived Units: The units which depend on the fundamental units or which can be expressed in terms of the fundamental units are called derived units. E.g. square metre, cubic metre - units of derived quantities - area, volume etc. 2 Systems of Units: In mechanics, length, mass and time are the three fundamental quantities. For the units of these three basic quantities, following systems have been used: (i) C.G.S. System: In this system, the unit of length is centimetre (cm), of mass is gram (g) and of time is second (s). (ii) F.P.S. System: In this system, the unit of length is foot (ft), of mass is pound (lb) and of time is second (s). (iii) M.K.S. System: In this system, the unit of length is (m), of mass is kilogram (kg) and of time is second (s) Later on more physical quantities were included as fundamental quantities and it is now called as standard international system of measurement i.e. S.I. Fundamental quantities, units and symbols in S.I. System Quantity Name of Unit and Symbol Length metre m Mass kilogram kg Time second s Temperature kelvin K Electric Current ampere A Amount of substance mole Mol Luminous intensity candela Cd Use of Standard Prefix with a unit: 3 Units of length: The S.I. unit of the length is metre (m) and C.G.S. unit is centimetre (cm). Sub units of metre: (i) centimetre (cm) : 1cm = 10-2 m (ii) millimetre (mm) : 1mm = 10-3 m (iii) micrometre or micron (μ): 1 μm = 10-6 m (iv) nanometre (nm) : 1 nm = 10-9 m Bigger units: (i) Astronomical unit (A.U.): One astronomical unit is equal to the mean distance between the Earth and the Sun. (ii) Light year (ly): A light year is the distance travelled by light in vacuum in one year. The distance of stars from the Earth is generally expressed in light years. Smaller Units: (i) Angstrom (A0): 1A0= 10-10 m = 10-8 cm = 10-1 nm (ii) Fermi (f) : 1 fermi = 10-15 m Units of mass: The S.I. unit of mass is kilogram (kg) and C.G.S. unit is gram (g). Smaller units: (i) gram (g): 1 g = 10-3 kg (ii) milligram (mg): 1 mg = 10-6 kg = 10-3 g Bigger units: (i) quintal: It is one hundred times a kilogram i.e. 1 quintal = 100 kg (ii) metric tonne: It is one-thousand times a kilogram i.e. 1 metric tonne = 1000 kg Units of time: The S.I. unit of time is second (s). Smaller units: Bigger units: (i) 1 ms = 10-3 s (ii) minute (min): 1 min = 60 s (iii) 1 µs (microsecond) = 10-6 s (iv) hour(h) : 1 hour = 60 min = 3600 s (v) day: 1 day = 24 h = 1440 min = 86400 s (vi) 1 shake = 10-8 s (vii) 1 ns = 10-9 s (viii) decade: 1 decade = 10 years 4 Guidelines for writing the units: (i) The symbol for a unit, which is not named after a scientist, is written in small letters. e.g. symbol for metre is m, second is s and so on. (ii) The symbol for a unit, which is named after a scientist, is written with the first letter of his name in capital. e.g. N for newton, J for joule, Pa for pascal and so on. (iii) The full name of the unit, irrespective of the fact whether it is named after a scientist or not, is always written with a lower initial letter. e.g. unit of mass kilogram not as Kilogram, unit of length metre not as Metre, unit of force is written as newton not as Newton. (iv) A derived unit formed by multiplication of two or more units is written after putting a dot, cross or leaving a space between the two symbols. e.g. N.m or N × m or N m (v) Negative power is used for derived units, which are formed by dividing one unit by the other. e.g. The unit of velocity is m/s. It is expressed as m.s-1 (vi) A unit in its short form is never written in plural. e.g. 10 metres cannot be written as 10ms, 10 kilograms cannot be written as 10 kgs. Measurement of Length Least count of measuring instrument: The least count of an instrument is the smallest measurements that can be taken accurately with it. A measuring instrument is provided with a graduated scale for measurement and the least count is the value of one smallest division on its scale. e.g. The least count of stop watch is 0.5 s if there are 10 divisions between 0 and 5s. The least count of geometry ruler is 1mm since 0 to 1 cm divided into 10 equal parts. Note: Smaller the least count of an instrument, more precise is the measurement made by using it. 5  Vernier Callipers Vernier callipers are also called the slide callipers. It is used to measure the length of rod, the diameter of a sphere, the internal and external diameters of a hollow cylinder, the depth of a small beaker etc. Diagram: Vernier callipers – main parts and their functions: PART FUNCTION 1. Main scale 1. To measure the length correct up to 1mm 2. Vernier scale 2. To measure the length correct up to 0.1mm 3. Outer/Outside/External jaws 3. To measure the length of a rod, diameter of a sphere, external diameter of a hollow cylinder 4. Inner/Inside/Internal jaws 4. To measure the internal diameter of a hollow cylinder or pipe 5. Tail/Strip/Projection 5. To measure the depth of a small beaker or a bottle 6 Principle of laboratory Vernier callipers: The main scale is graduated with a value of one division on it equal to 1 mm. There are 10 divisions on the Vernier scale which exactly coincides with the 9 divisions on the main scale i.e. 9 mm. Therefore each smallest division of the vernier scale = 9/10 = 0.9 mm The graduations on the Vernier scale are such that the length of n divisions on the Vernier scale is equal to the length of (n-1) divisions of the main scale. Least count of Vernier callipers: The least count of vernier callipers is defined as the difference between the values of one main scale division and one vernier scale division. Value of one main scale division (1 M.S.D) = 1mm Value of one vernier scale division (1 V.S.D) = 0.9 mm L.C. = 1 M.S.D – 1 V.S.D L.C. = 1 – 0.9 L.C. = 0.1 mm L.C. = 0.01 cm Let n divisions on Vernier be of length equal to that of (n-1) divisions on main scale. Let the value of 1 main scale division be x. Value of n divisions on Vernier = (n-1) x Value of 1 division on Vernier = (n-1) x/n L.C. = x - (n-1) x/n L.C. = x/n i.e., L.C. = Value of one main scale division (x) /Total number of divisions on Vernier Zero error in vernier callipers In the closed position of the jaws, if the zero mark of the Vernier scale exactly coincides with the zero mark of the main scale, then Vernier callipers is said to be free from zero error. In this condition, the end of strip T also touches the end of the main strip. But sometimes there is a mechanical error in the Vernier callipers due to which the zero mark of the vernier scale does not coincide with the zero mark of the main scale in the closed position of the jaws. It is then said the Vernier callipers have zero error. 7 Kinds of zero error: (i) Positive zero error: In a closed position of the jaws, if the zero mark of the Vernier scale is on the right of the zero mark of the main scale, then the zero error is said to be positive. Positive zero error = 6 × L.C. = 6 × 0.01 = 0.06 cm (ii) Negative zero error: In a closed position of the jaws, if the zero mark of the Vernier scale is on the left of the zero mark of the main scale, then the zero error is said to be negative. Negative zero error = – (10 – 6) × L.C. = – 4 × 0.01 = – 0.04 cm 8  Micrometer Screw Gauge Screw gauge is a measuring instrument made out of a calibrated screw used to measure small objects' dimensions. A screw gauge is used for the precise measurement of thin wires and sheets. It consists of two scales: a Pitch Scale and a Circular Scale. In a simple laboratory micrometer screw gauge there are 100 divisions on a circular scale and the pitch of the screw is 1 mm. So when one complete rotation is completed the 100 divisions are covered through a distance of1 1 mm so if we turn the screw through 1 rotation then the screw advances by 100 th of a millimetre. Pitch of a screw gauge is the linear distance moved by its screw on the main scale when the circular scale is given one complete rotation. Circular scale is horizontally engraved on the thimble. A revolution of the circular scale is equivalent to about half a millimeter of screw displacement. L.C of M.S.G. = 𝑃𝑖𝑡𝑐ℎ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠 𝑜𝑛 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑠𝑐𝑎𝑙𝑒 = 1 100 mm = 0.01mm = 0.001cm Backlash error. Due to wear and tear of threads of the screw, if we turn the thimble, only the thimble rotates but the screw advances after remaining stationary for a while. This error is called a backlash error. It cannot give you correct reading. To avoid this while using the instrument, turn the screw only in one direction. 9