Title 1. UNITS AND MEASUREMENT.pdf ✅

UNIT-I PHYSICAL WORLD AND MEASUREMENT UNITS AND MEASUREMENT Need for measurement : Units of measurement; systems of units; S.I. units; fundamental and derived units; significant figures. Dimensions of physical quantities; dimensional analysis and its applications.. Topic-1 Units System and Measurement Revision Notes  Units : It is the chosen standard of measurement of a quantity which has essentially the same nature as that of the quantity.  Fundamental Units : The physical quantities which are independent of each other and which can represent remaining physical quantities are called fundamental physical quantities and their units are called fundamental units. Seven Fundamental physical quantities in SI system of units are : (a) Mass - kg (Kilogram) (b) Length - m (Meter) (c) Time - s (Second) (d) Temperature - K (Kelvin) (e) Electric current - A (Ampere) (f) Luminous Intensity - cd (Candela) (g) Amount of substance - mol (Mole)  Derived Units : These are the units of measurement of all other physical quantities which can be obtained from fundamental units, e.g., Velocity - (m/s), Acceleration - (m/s2 ), Pressure - (Pa), Force - (N) and so on.  Unit system (a) F. P. S. system : Foot, Pound, Second. (b) C. G. S. system : Centimetre, Gram, Second. (c) M. K. S. system : Meter, Kilogram, Second.  Significant figures : The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.  Rules for significant figure : (a) All non-zero digits are significant. 198745 contains six significant digits. (b) All zeros those occur between any two non-zero digits are significant. For example, 108.0097 contains seven significant digits. (c) All zeros those are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00798 contained three significant digits. (d) All zeros those are on the right of a decimal point are significant, only if, a non-zero digit does not follow them. For example, 20.00 contained four significant digits. Syllabus TOPIC - 1 Units System and Measurement TOPIC - 2 Dimensional Analysis 1 CHAPTER
UNITS AND MEASUREMENT (e) All the zeros those are on right of the last non-zero digit, after the decimal point, are significant. For example, 0.0079800 contains five significant digits. (f) All the zeros that are on the right of the last non-zero digit are significant if they come from a measurement. For example, 1090 m contains four significant digits. Key Words  Fundamental Units : Units of the physical quantities which are independent of each other and which can represent remaining physical quantities.  Derived Units : Units of measurement of those physical quantities which can be obtained from fundamental units. Key Formulae  1 AU = 1.496 × 1011 m.  1 ly = 9.46 × 1015 m.  1 parsec = 3.1 × 1016 m.  1 Å = 10–10 m; 1 nm = 10–9 m 1 μm = 10–6 m, 1 mm = 10–3 m  60 seconds (of arc) = 1 min (arc)  60 min. (of arc) = 1 degree (of arc)  180 degree (of arc) = p radian  Indirect methods for long and small distances : Angular diameter (θ) = d D d = diameter, D = distance, radius = r  Magnification : (a) Linear Magnification = Size of image Size of object (b) Linear Magnification = Areal Magnification Mnemonics Concept: The fundamental quantities of SI system: Mnemonics: At the last moment she luckily caught the train. Interpretation: A - Amount of substance t - Temperature (thermodynamic) l - Length m - Mass lu - Luminous intensity c - Current t - Time Very Short Answer Type Questions (1 mark each) Q. 1. Define radian. R [NCT 2008] Ans. One radian is the angle subtended at the centre of the circle by an arc equal in length to the radius of the circle. 1 Q. 2. Express one micron in metre. A [NCT 2010] Ans. 1 micron = 10–6 metre 1 Q. 3. What is the number of significant figures in 0.06070 ? U Ans. 4. 1 Q. 4. Which of the following reading is most accurate ? (a) 7,000 m, (b) 7 × 102 m, (c) 7 × 103 m. A Ans. (a) 7,000 m. 1 Q. 5. The mass of a body as measured by two students is given as 1.2 kg and 1.23 kg. Which of the two is more accurate and why ? A Ans. The second measurement is more accurate as it has more number of significant figure. 1 Q. 6. Name the supplementary units of S.I. system. R Ans. (i) Radian (rad) for plane angle. 1⁄2 (ii) Steradian (sr) for solid angle. 1⁄2
Oswaal CBSE Question Bank Chapterwise & Topicwise, PHYSICS, Class-XI Short Answer Type Questions-I (2 marks each) Q. 1. Find the number of times the heart of a human being beats in 10 years. Assume that the heart beats once in 0.8 sec. A Ans. In 0.8 s, the human heart makes one beat. ∴ In 1 s the human heart makes = 1 0.8 = 10 8 beats. 1 ∴ In 10 years the human heart makes = 10 8 × 10 × 365 × 24 × 60 × 60 beats = 3.942 × 108 beats. 1 Commonly Made Error Students commits mistake while finding beats in one second and seconds in one year. Answering Tip Students should carefully find the number of beats in one second and then multiply the same with the number of seconds in an year. Q. 2. Derive S.I. unit of Joule (J) in terms of fundamental units. U Ans. Joule is a unit of work. Using the relation, Work = force × displacement = mass × acceleration × displacement = velocity mass× ×displacement time = mass × displacement×displacement time×time = mass × displacement2 × time–2 1 Unit of work, J = kg × m2 × s–2 = kgm2 s–2. 1 Q. 3. Give conversion of the some commonly used large units of length into metre. U Ans. 1 Light year (ly) = 9.46 × 1015 m 1 Astronomical unit (AU) = 1.496 × 1011 m 1 Parallactic second (parsec) = 3.08 × 1016 m 2 Q. 4. Why an optical microscope is not used to measure the size of a molecule ? U Ans. Size of molecule ranges from 10–8 m to 10–10 m. An optical microscope uses visible light of average wavelength 6000 Å, i.e., 6000 × 10–10 m to measure the sizes. Since, size of molecule is smaller than the wavelength of light used, so optical microscope cannot resolve a molecule. 2 Q. 5. Give conventional rules for the rounding off of uncertain digits. U Ans. The conventional rules are : (i) If the insignificant digit to be dropped is more than 5, the preceding digit is increased by 1, but if it is less than five, then preceding digits is not changed, e.g., 1.748 is rounded off to 3 significant figures as 1.75 and 1.742 as 1.74. 1 (ii) If the insignificant digit to be dropped is 5, then this digit is simply dropped if the preceding digit is even but if odd, then the preceding digit is increased by 1. e.g., the number 1.845 rounded off to three significant digits is 1.84 but for number 1.875 it is 1.88. 1 Short Answer Type Questions-II (3 marks each) Q. 1. What is system of units ? Mention some of them. R Ans. In general, a complete set of base units as well as derived units is called system of units. But, it was a practice to name the system of units after three fundamental units of length, mass and time only, e.g., (a) FPS system : In this system length is measured in foot (f), mass in pound (p) and time in second (s). So, this system is called FPS system. This system is also known as British Engineering system of units or simply British system of units. (b) C.G.S. system : In this system length is measured in centimeter (cm), mass in gram (g) and time in second (s), so this system is called C.G.S. system. (c) M.K.S. system : In this system length is measured in metre (m), mass in Kilograms (kg) and time in second (s), so this system is called M.K.S. system or metric system. (1 mark each) Q. 2. What is a prefix ? Give some common prefixes for multiples and submultiples. R Ans. Prefix is used to increase or decrease the value of a fundamental or derived unit as per practical requirements. Multiples Submultiples Exa (E) = 1018 atto (a) = 10–18 Peta (P) = 1015 femto (f) = 10–15 Tera (T) = 1012 pico (p) = 10–12 Giga (G) = 109 nano (n) = 10–9
UNITS AND MEASUREMENT Mega (M) = 106 micro (μ) = 10–6 Kilo (k) = 103 milli (m) = 10–3 Hecto (h) = 102 centi (c) = 10–2 Deca (da) = 101 deci (d) = 10–1 3 Commonly Made Error Students generally replace some multiples with submultiples and vice versa. Answering Tip Students should ensure the correctness of multiples and submultiples along with their prefixes used. Q. 3. List the S.I. base quantities and find their units with symbols. R Ans. S. No. Base quantity S.I. unit Symbol (i) Length metre m (ii) Mass kilogram kg (iii) Time second s (iv) Electric current ampere A (v) Temperature kelvin K (vi) Amount of substance mole mol (vii) Luminous intensity candela cd (1⁄2 mark each for any six points) Long Answer Type Questions (5 marks each) Q. 1. Write the S. I. units of the following physical quantities— (a) Luminous intensity, (b) Temperature, (c) Plane angle, (d) Electric current, (e) Amount of substance, (f) Solid angle, (g) Pressure. R Ans. (a) candela (cd) (b) kelvin (K) (c) radian (rad) (d) ampere (A) (e) mole (mol) (f) steradian (Sr) (g) N/m2 = pascal (pa) 5 Q. 2. What do you understand by the following : (a) Century, (b) Shake, (c) Lunar month, (d) Leap year, (e) Tropical year. R Ans. (a) It is the largest unit of time. 1 century = 100 years. (b) It is the smallest unit of time, 1 shake = 10–8 s. (c) It is the time taken by the Moon to complete one revolution around the Earth. 1 lunar month = 29.53 days. (d) A year which is divisible by 4 and in which the month of February is of 29 days is called leap year. Also a year is leap year if it is visible by 100 and also by 400. If the year is divisible by 100 but not by 400, then the year is not a leap year. (e) The year in which total solar eclipse takes place is called tropical year. (1 mark each) Topic-2 Dimensional Analysis Revision Notes  Dimensional analysis is the study of relationship between physical quantities and the fundamental quantities.  Dimensional equation is the equation expressing of the relationship between physical quantities and the fundamental quantities.  Principle of homogeneity: Dimensions of each term of a dimensional equation on both side should be same.  Conversion of units from one system to another: n1 and n2 be the magnitudes of a physical quantity in two systems respectively. General dimensions of the physical quantity be [Ma Lb TC]. If dimensions in two system be u1 = [M1 a L1 b T1 c ] and u2 = [M2 a L2 b T2 c ] respectively then n1 [M1 a L1 b T1 c ] = n2 [M2 a L2 b T2 c ]  Dimensional analysis used to derive formula of a physical quantity.  Correctness of formula of a physical quantity may be checked using principle of homogeneity.