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# The Unit Of Measurement

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### The Unit Of Measurement

1. 1. Introduction Physics is an experimental science. Theories are useful only if their predictions agree with the results of experiments. So measurement plays an important part in physics. Together with other scientists , physicists have agreed on a single system of units for the measurement of physical quantities . A physical quantity is clearly defined with a numerical value and a unit. A physical quantity can be measured using a standard size called the unit. Units identify the quantity that has been measured. The standard size used must (i) be easily reproduced (ii) not have its magnitude changed (iii) be internationally accepted Although various systems of units have been used over the years, scientists have generally agreed to use the International System of Units (S.I. Unit). Units for the base quantities are known as base units, i.e. metre , kilogram, second, Kelvin and ampere. The definition of base units. The metre is the length of the path traveled by light in vacuum during a time interval of 1 of a second 299792458 The kilogram is the mass of a prototype cylinder of platinum-iridium alloy that is kept at the International Bureau of Weights and Measures. The second is 9192631770 periods of a specified radiation from Cesium-133 atoms The Kelvin is 1 of the 273.16 thermodynamic temperature of the triple point of water The ampere is the current carried by two long parallel wires placed one meter apart, when the attractive force per unit length between two wires is 2 x 10-7 Nm-1 . Prefixes Prefix is a scientific notation word before the base units and have certain value uses powers of 10. Prefix Symbol Factor Tera Giga Mega Kilo Desi Centi Mili Mikro Nano Piko T G M k d c m µ n p Standard Form The radius of earth 6400000000 mm and the diameter a metal wire is 0.00000045 km. What is the best way to write these numbers ? The best way is try to write the numbers in shorthand form. The shorthand form of writing numbers is called standard form. In general, the standard form number is a x 10n where 1 ≤ a<10 and n are positive integers or negative integers. 6 LESSON 2 Units Of Measurement
2. 2. Example 1 Write the following numbers in standard form. (a) 0.00008 m (b) 5300 g (c) 0.0068 cm (d) 567.13 km (e) 345.2 x 104 m (f) 0.000078 x 10-6 s (g) 7 x 10-5 x 8 x 106 (h) 3 x 108 + 8 x 106 (i) 6.2 x 109 (j) 3.8 x 10-2 - 7.2 x 10-3 3.1 x 103 Solution Example 2 Convert the following lengths into the units of metre. (a) 2.3 km (b) 0.62 mm (c) 3 x 106 cm Solution Example 3 Express 22.5 g in the units of (a) kg (b) dg Solution Example 4 Express (a) 73 kg in terms of mg (b) 0.0045 ms in terms of Ms Solution Example 5 Convert (a) 11.5 cm3 into the units of m3 (b) 72 km h-1 into the units of ms-1 (c) 5 g cm-3 into the units of kg m-3 Solution 7
3. 3. 1 Which of the following is not true? A The metre is the length of the path traveled by light in vacuum during a time interval of 1 of a second 299792458 B The kilogram is the mass of a prototype cylinder of copper-aluminium alloy that is kept at the International Bureau of Weights and Measures. C The second is 9192631770 periods of a specified radiation from Cesium-133 atoms D The kelvin is 1 of the 273.16 thermodynamic temperature of the triple point of water 2 Every number can be written in ‘standard form’, particularly in the cases of A very small numbers B very large numbers C very small and very large numbers 3 The standard form for 15200 is A 15.2 x 10 2 B 1.52 x 10 3 C 1.52 x 10 4 D 0.152 x 10 -4 E 1.52 x 10-5 4 The product of 2.4 x 10 -2 and 5.0 x 10 - 4 is A 1.2 x 10 6 B 1.2 x 10 5 C 1.2 x 10- 5 D 1.2 x 10- 7 E 1.2 x 10 -8 5 If A = 2 x 10 - 4 and B = 3 x 10 - 5 then the value of A + 5B is A 1.7 x 10 - 5 B 3.5 x 10 - 5 C 1.7 x 10 - 4 D 3.5 x 10 - 4 E 1.7 x 10 –3 6 What is 0.0455 kg expressed in standard form? A 0.455 x 10 - 1 kg B 4.55 x 10 - 2 kg C 45.5 x 10 - 3 kg D 455 x 10 - 4 kg 7 The prefixes according to their value in ascending order are A Giga,mega,kilo,centi B Mikro,mili,centi,kilo C Mega,giga,kilo,centi D Centi,giga,mikro,mili 8 Radio 5 RTM station operates at 105 .6 M Hz. The expression of the frequency in units of Hz is A 1.056 x 10 8 Hz B 1.056 x 10 6 Hz C 1.056 x 10 4 Hz D 1.056 x 10 - 4 Hz E 1.056 x 10 - 8 Hz 9 5 x 10 - 4 seconds is equivalent to A 0.05 microseconds B 0.5 microseconds C 50 microseconds D 500 microseconds E 5000 microseconds 10 Which one of the following measurements is different? A 2.3 x 10 2 m B 2.3 x 10 4 cm C 2.3 x 10 6 mm 11 Which one of the following measurements is smallest ? A 1.5 x 10 2 kg B 1.5 x 10 7 g C 1.5 x 10 12 µ g 8 TUTORIAL 2
4. 4. 12 The misprints of length according to their value in ascending order are A 7 x 10 - 4 km , 7 x 10 2 cm , 7 x 10 4 mm B 7 x 10 2 cm , 7 x 10 4 mm , 7 x 10 - 4 km C 7 x 10 4 mm , 7 x 10 - 4 km , 7 x 10 2 cm 13 The volume of a metal sphere is 12 cm 3. This volume in units of m 3 is A 1.2 x 10 - 2 B 1.2 x 10 - 3 C 1.2 x 10 - 5 D 1.2 x 10 – 7 E 1.2 x 10 - 9 14 The velocity of a car is 108 km h-1. What is the velocity in units of ms-1 ? A 20 B 30 C 50 D 60 E 90 15 The pressure exerted by a box on a surface is 500 N cm – 2 . What is the pressure in units of Pa? ( 1 Pa = 1 N m - 2 ) A 5 x 10 - 2 B 5 x10 -1 C 5 x 10 4 D 5 x 10 6 E 5 x 10 8 16 The acceleration of a trolley is 2000 cm s- 2 This acceleration in S.I. unit is A 0.002 B 0.02 C 0.2 D 2 E 20 17 Which one of the following prefixes is less then 1? A Mega B Desi C Kilo 18 Which of the following is true? A 0.00023 = 2.3 x 10 - 3 B 0.05 = 5 x 10 - 1 C 3450 = 3.450 x 10 4 D 46.531 =4.6531 x 10 4 E 5678.9 = 5.6789 x 10 3 19 Value of physical quantities S.I. unit 400 cm 2 m 2 216 km h -1 ms -1 4 mm 3 m3 1500 cm s -2 ms - 2 Complete the table above. 20 Readings 7.2 x 10 5 µm , 7.2 x 10-2 cm 7.2 x 103 mm and 7.2 x 10 - 6 km The table above shows the measurement of length for four different objects. (a) Which reading is the longest ? .................................................................... (b) Which reading is the shortest? .................................................................... (c) Arrange the readings according descending order. .................................................................... .................................................................... (d) Which reading is more than 1 metre? .................................................................... (e) A cube of sides 7.2 x 103 mm . State the volume of the cube in unit of m3 9