Master the Fundamentals of Physics with a Board-Focused Approach!

Physical Quantities and Measurement

Q#1: What is physics? In what ways does physics contribute significantly to science, technology, and society? Ans: Physics: Physics represents the scientific field dedicated to exploring the physical cosmos, encompassing energy, matter, and their interconnections. Explanation: Engaging in physics allows us to grasp our immediate surroundings, our inner selves, and the distant realms. It spans numerous occurrences, from minuscule subatomic elements to vast galaxies and the cosmos as a whole. Physics and Science: Physics serves as the foundation for all scientific disciplines. The bulk of key breakthroughs in areas like chemistry, biology, geology, agriculture, environmental studies, astronomy, engineering, and medicine originate from physicists' efforts. Physics, Technology, and Its Influence on Society: Physics focuses on acquiring and structuring information. Technology enables people to apply this information in real-world scenarios. Every technological advancement stems from physical principles, making physics essential for human advancement and elevating living conditions. Example #1: Physics offers essential insights for inventing advanced medical tools, including computed tomography (CT) scans, magnetic resonance imaging (MRI), and laser systems. Example #2: The application of physics in information systems has raised communication quality. Cellular phones are widely utilized, even by those without formal education. Holographic techniques produce three-dimensional visuals. Example #3: Physics examines the movement of electrons and spacecraft, the power in acoustic waves and electrical networks, the composition of protons, and the overall structure of the cosmos. Q#2: What does SI stand for? List the SI fundamental quantities and their corresponding units. Ans: International System of Units: In 1960, a global meeting occurred near Paris, France, where a universal measurement framework was established. This was named the International System, commonly abbreviated as SI units. Within this framework, seven core quantities were selected as fundamentals. Their units are precisely defined and termed base units, serving as the basis for deriving all others. The seven fundamental physical quantities, along with their SI base units and symbols, are listed in the table below. Base QuantitySI Base UnitSymbol of SI UnitLengthMetermMassKilogramkgTimeSecondsElectric currentAmpereATemperatureKelvinKAmount of substanceMolemolLuminous intensityCandelacd Q#3: What do physical quantities mean? Differentiate between fundamental and derived physical quantities. Ans: Physical Quantities: Any quantities that are measurable are referred to as physical quantities. Example: Examples include length, mass, time, density, temperature, and others. Distinction between Fundamental and Derived Physical Quantities: Fundamental QuantitiesDerived QuantitiesThe smallest set of physical quantities whose units are defined and standardized, allowing expression of all other quantities in their terms, are known as fundamental quantities.Physical quantities expressed using fundamental quantities are termed derived quantities.There are seven such quantities.These are unlimited in number, without a fixed count.Examples: Length, mass, time, electric current, temperature, amount of substance, and luminous intensity.Examples: Velocity, area, volume, density, work, momentum, and similar. Q#4: What does standard form or scientific notation refer to? Ans: Scientific Notation: Scientific notation provides a method for expressing extremely large or small numbers that are challenging to write in regular decimal format. Explanation: A substantial or minute number 'N' can be represented as a product of a digit 'M' and a power of 10, as follows: $$N = M times 10^n$$ Here, 'M' is a value with a non-zero initial digit, and 'n' indicates the exponent of 10, which could be positive or negative. Example: The moon's mass is roughly 70,000,000,000,000,000,000,000,000 kg, expressed in standard or scientific notation as $7 times 10^{22}$ kg. Likewise, an atomic nucleus's diameter is approximately 0.0000000000000001 m, noted in standard or scientific notation as $1 times 10^{-14}$ m. Q#5: What are prefixes? Provide an explanation with examples. Ans: Prefixes: Prefixes are a system for denoting very tiny or very huge numbers using powers of 10, assigning them appropriate names. Explanation: Prefixes precede a base unit to indicate the magnitude by which the physical quantity exceeds or falls short of the base unit for that quantity. Prefixes simplify the notation of standard forms. Large values are conveniently expressed using suitable prefixes alongside units. Examples: Paper thickness is more easily noted in the smaller millimeter unit rather than meters. In the same way, the considerable distance separating two cities is better conveyed in the larger kilometer unit. A practical list of prefixes appears in the table: Decimal MultiplierPrefixSymbolDecimal MultiplierPrefixSymbol10¹⁸ExaE10⁻¹decid10¹⁵PetaP10⁻²centic10¹²TeraT10⁻³millim10⁹GigaG10⁻⁶microμ10⁶MegaM10⁻⁹nanon10³KiloK10⁻¹²picop10²HectoH10⁻¹⁵femtof10¹DecaDa10⁻¹⁸attoa Q#6: Explain the design and application for measuring with these tools: a. Vernier Caliper b. Screw Gauge Ans(a): Vernier Caliper: A tool that measures tiny fractions of the tiniest scale mark by moving one scale across another is termed a vernier caliper. Design: Vernier calipers feature two scales. Main Scale: This scale typically has 1mm intervals and includes jaw A at its left extremity. Vernier Scale: The sliding vernier scale features intervals that are a multiple of the main scale's marks. It generally spans 9mm, split into 10 equal parts. The gap between vernier lines is 9/10 mm = 0.9mm. It includes jaw B at its left extremity. Vernier Constant or Least Count: The smallest accurate measurement possible with vernier calipers is known as its vernier constant or least count. It is determined by: $$text{Least count} = frac{text{Smallest division on main scale}}{text{Total no. of divisions on vernier scale}}$$ With a 1mm smallest main scale division and 10 vernier divisions, the least count becomes: $$begin{aligned} text{Least count} &= frac{1 text{mm}}{10} \ &= 0.1 text{mm} \ &= 0.01 text{cm} end{aligned}$$ Applications of Vernier Caliper: Vernier calipers serve to precisely measure short lengths up to 0.1mm or 0.01cm. They can assess an object's thickness, diameter, or width, as well as a hollow cylinder's inner and outer diameters. (b). Screw Gauge: A device measuring small fractions of the smallest scale mark via circular scale rotation is called a screw gauge. Design: A screw gauge includes a U-shaped structure linked to a hollow tube at one end. The tube contains a threaded nut. A long flat-faced stud fits this nut. Opposite this, another flat-faced stud attaches to the U-frame's other end. Both studs' faces align parallel. The smaller stud is the anvil, the larger the spindle. The anvil stays fixed, the spindle rotates. The measured item sits between anvil and spindle. Least Count of Screw Gauge: The tiniest accurate length measurable by screw gauge is its least count. It is computed by dividing the pitch (linear distance per rotation) by circular scale divisions. $$text{Least count} = frac{text{Pitch of Screw Gauge}}{text{Total no.of division on circular scale}}$$ For a 0.5mm pitch and 50 circular divisions, Least Count = 0.5 mm / 50 = 0.01 mm or 0.001 cm Applications of Screw Gauge: Screw gauges measure very brief lengths like sheet metal thickness or wire diameter up to 0.01mm or 0.001cm. Q#7: What does significant figures in measurements signify? What key aspects should be considered when identifying significant figures in a measurement? Ans: Significant Figures: Significant figures consist of all reliably known digits plus the initial uncertain digit. Explanation: Values fall into exact and measured categories. Exact values are clearly countable, such as noting 3 pencils or 2 books, where we state the precise count. Measured values, however, carry some uncertainty. For instance, measuring a pencil with a 1mm least count ruler shows it exceeds 67mm but is below 68mm. Estimating 67.5mm means accuracy to 67mm, but the 0.5mm is approximated. The final digit might err, termed the uncertain digit. Basic Rules for Significant Figures: Digits from 1 to 9 are always significant. For instance, 47.73 has four significant figures. A zero between significant digits is significant. For example, 32.50063 has seven significant figures. Leading zeros before significant digits are insignificant. For example, 0.00467 has three significant figures. Trailing zeros after significant digits may or may not count. In decimals, trailing zeros are significant. For example, 7.400 has four. In 80,000, significant figures could be 1, 2, or up to 5. In scientific or standard notation, digits excluding the power of ten are significant. Electron mass $9.11 times 10^{-31}$ kg has three significant figures. Guidelines for Rounding Significant Figures: a. Drop a last digit below 5 without change, e.g., 2.6573 rounds to 2.657. b. If the dropped digit exceeds 5, add 1 to the kept digit, e.g., 2.6578 rounds to 2.658. c. For a dropped 5 with an even kept digit, drop it unchanged, e.g., 2.6585 rounds to 2.658. d. For a dropped 5 with an odd kept digit, add 1 to the kept digit, e.g., 2.6575 rounds to 2.658. Q#8: Explore the role of Muslim scholars in advancing physics. Ans: Islamic scholars made substantial contributions to physics development. Notable figures include: YAQUB KINDI (800-873 AD) Born in Basra, Iraq, he contributed significantly to meteorology, specific gravity, and tides. His primary achievements were in optics, particularly light reflection. IBNAL HAITHAM (965-1039 AD) Born in Basra, Iraq, he was a prominent scholar. His major optics work is the book Kitab-ul-Manazir. He is regarded as the pinhole camera's inventor. AL-BERUNI (973-1048 AD) An Afghan intellectual who authored 150 books on physics, cosmology, geography, culture, archaeology, and medicine. Al-Beruni examined Earth's shape, solar and lunar movements, and lunar phases. Q#9: Examine the contributions of renowned Pakistani physicists. Ans: Dr. Abdus Salam (1926-1996) Born in Jhang in 1926, he was a theoretical physicist from Pakistan. He co-won the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for electroweak unification theory. He was Pakistan's first Nobel laureate in science. Dr. Abdul Qadeer Khan Born in Bhopal, India, in 1936, he is a Pakistani nuclear physicist and metallurgist who initiated Pakistan's uranium enrichment for its atomic program. He established Kahuta Research Laboratories (KRL) in 1976, serving as senior scientist and Director-General until 2001 retirement. Q#10: What is physics? Outline the primary branches of physics. Ans: Physics: Physics is the scientific branch addressing matter's properties, energy, and their interrelations. Branches of Physics: Mechanics: This physics area studies material objects' motion influenced by forces. Examples: Dropping items, friction, mass, rotating bodies. Heat and Thermodynamics: This physics domain explores heat, temperature, their energy links, and heat conversion to other energy types. Examples: Melting/freezing, motors, cooling devices. Oscillations and Waves: This physics segment investigates back-and-forth motions and wave characteristics. Examples: Spring-mass setups, aquatic waves, acoustic waves, etc. Optics: This physics field covers light's essence, travel, reflection, bending, scattering, and wave traits. Examples: Reflectors, optics, scopes, vision. Electricity and Magnetism: This physics branch analyzes stationary and dynamic charges plus related events. Examples: Electric charge, wiring, magnets, electromagnets. Atomic and Nuclear Physics: This physics area delves into atoms' and nuclei's structures and attributes. Examples: X-rays, lasers, atomic reactors, MRI, CT, PET scans. Relativity: This physics domain handles high-speed objects and gravity. Examples: Accelerators for particles, atomic power. Quantum Physics: Quantum physics examines indivisible energy units called quanta per quantum theory. Examples: Atoms and components. Particle Physics: This physics branch investigates particles forming matter and radiation. Examples: Quarks, leptons, photons, bosons, etc. Cosmology and Astrophysics: This addresses the universe's beginning, development, and destiny. Examples: Celestial bodies, star clusters, voids. Biophysics and Medical Physics: This explores physical aspects of biology and physics in health, like prevention, detection, treatment. Examples: MRI, CT scans, radioisotopes, cellular conduction. Q#11: What are physical quantities? Elaborate on their categories. Ans: PHYSICAL QUANTITIES: Measurable quantities are known as physical quantities. Examples: Length, mass, time, density, temperature, etc. CATEGORIES OF PHYSICAL QUANTITIES: Physical quantities divide into two groups: Fundamental physical quantities Derived physical quantities FUNDAMENTAL PHYSICAL QUANTITIES: The minimal physical quantities with defined, standardized units, enabling expression of others, are fundamental quantities. Seven exist: mass, length, time, current, temperature, luminous intensity, substance amount. BASE UNITS: In SI, seven quantities are fundamentals with defined, standardized units called base units. OR Base quantities' units are base units. The seven fundamental quantities, SI units, symbols: NameSymbolNameSymbolLengthlMetermMassmKilogramkgTimetSecondsElectric currentIAmpereATemperatureTKelvinKLuminous intensityICandelacdAmount of substancenMolemol DERIVED PHYSICAL QUANTITIES: Quantities defined via fundamentals are derived. Examples: work, area, volume, speed, power, etc. DERIVED UNITS: Units from base unit multiplication/division are derived. In SI, all others derive from seven bases. Some derived examples: NameSymbolNameSymbolAreaASquare meterm²SpeedvMeter per secondm s⁻¹ForceFNewtonN=kg m s⁻²EnergyE, UJouleJ=kg m² s⁻²PressurePPascalPa=kg m⁻¹ s⁻² Q#12: What is a unit system? Ans. UNIT SYSTEM: A full collection of units for every physical quantity is a unit system. Multiple systems exist. For instance: Meter-kilogram-second (MKS) Foot-pound-second (FPS) The global standard is System International (SI). Q#13: What are measurement tools? Ans. MEASUREMENT TOOLS: Tools for quantifying physical attributes are measurement instruments. Physicists employ many, from basic rulers and timers to advanced like atomic force microscopes (AFM) and scanning tunneling microscopes (STEM). All have measurement constraints. LEAST COUNT: The smallest measurable scale value on an instrument is its least count. Q#14: What is a meter rule? Ans. A meter rule measures object lengths or point distances. Made from varied materials in diverse sizes. Q#15: Outline the function, build, and measurement use of vernier calipers. Ans. VERNIER CALIPERS: A sliding scale tool for fractional smallest divisions is a vernier caliper. FUNCTION: Used for length, thickness, diameter, width, hollow cylinder diameters (inner/outer), depths. BUILD: Two scales: main and vernier. MAIN SCALE: 1mm marks typically, left jaw A. VERNIER SCALE: Multiples of main marks, 9mm length into 10 parts. 0.9mm line gap. Left jaw B. VERNIER CONSTANT OR LEAST COUNT: Smallest accurate vernier measurement. Formula: $$text{Least count} = frac{text{smallest division on main scale}}{text{total no.of divisions on vernier scale}}$$ 1mm main, 10 vernier: 1mm/10 = 0.1mm = 0.01cm ZERO ERROR: Closed jaws may not align zeros. Misalignment means zero error. POSITIVE ZERO ERROR: Vernier zero right of main zero. NEGATIVE ZERO ERROR: Vernier zero left of main zero. FINDING ZERO ERROR: Close jaws, note vernier coinciding main division “n”, multiply by least count. ZERO CORRECTION: Subtract positive, add negative from reading. MEASUREMENT WITH VERNIER CALIPERS: For small cylinder diameter: Check zero error. Place object, tighten jaws. Main reading “x”. Vernier coinciding “y” = division × least count. Sum x+y. Adjust ± zero error. Accurate = (x+y) ± zero error. Q#16: Detail the function, build, and measurement use of screw gauge. Ans. SCREW GAUGE: Rotary circular scale for fractional smallest divisions is screw gauge. BUILD: U-frame with hollow tube, threaded nut. Long flat stud in nut. Opposite small flat stud. Parallel faces. Anvil small, spindle long. Anvil fixed, spindle moves. Object between. PITCH OF SCREW GAUGE: Linear distance per rotation. LEAST COUNT OF SCREW GAUGE: Smallest accurate length. Pitch / circular divisions. 0.5mm pitch, 50 divisions: 0.5/50 = 0.01mm or 0.001cm ZERO ERROR: Anvil-spindle meet, thimble zero not on datum: zero error. POSITIVE ZERO ERROR: Circular zero below horizontal. NEGATIVE ZERO ERROR: Circular zero above horizontal. FINDING ZERO ERROR: Rotate bolt to stud touch. Circular coinciding horizontal “n” × least count = zero error. ZERO CORRECTION: Add negative, subtract positive for correct. MEASUREMENT WITH SCREW GAUGE: For small sphere diameter: Check zero error. Place object, tighten via thimble. Linear reading “x”. Circular coinciding “y” = division × least count. Sum x+y. Adjust ± zero error. Accurate = (x+y) ± zero error Q#17: What is physical balance? Ans. PHYSICAL BALANCE: Tool for body mass measurement. EXPLANATION: Common balance with pans: object one pan, known weight other. Sensitive for milligram accuracy, glass-enclosed against dust/wind. Q#18: What is a stopwatch? Discuss types and operations. Ans. STOPWATCH: Device for specific time intervals. Two types: Mechanical/Analog Digital MECHANICAL/ANALOG STOPWATCH: Small minute, long second hands. Circular dial scales. OPERATION: Zero hands via knob press/release. Press/release starts. Second hand two 30s rotations advances minute one. Push knob stops, note time. DIGITAL STOPWATCH: Digital display clock. OR Digits show time. OPERATION: Two buttons control timing. Top starts/stops, elapsed displayed. Second resets to zero. Also records splits/laps. Split freezes display for reading, mechanism continues. Second split resumes total display. Q#19: Discuss function, build, working of measuring cylinder. Ans. MEASURING CYLINDER: Device for liquid volume or irregular solid volume like key. BUILD: Transparent plastic/glass, vertical ml or cm³ scale. WORKING: Pour water half full, note volume. Lower object fully immersed, note new volume. Object volume = new - initial. Conceptual Questions Q#1: How is technology influenced by physics? Ans: Physics and technology interlink closely. Physics gathers/organizes knowledge. Physical principles underpin technologies. For example: Transport like buses, cars, bikes based on mechanics. Heat engines on thermodynamics. Computers on physics principles. Electromagnetic induction for generators. Nuclear fission for power plants. Medical tools like CT, MRI, LASER from physics. Physics crucially develops technologies. Q#2: Physics and biology differ as science branches; how does physics connect to biology? Ans: Physics aids biology greatly, e.g.: i. Inventions like microscopes, electron microscopes, CT scans, ultrasounds, X-rays. ii. Concave/convex lenses correct vision defects. iii. Muscle/bone motion follows physics (levers). iv. Photosynthesis understood via light nature. Q#3: Why matter measurements? Ans: Measurement fundamental in science. Physics involves measurable quantities, standardizing daily aspects. Examples: Measurements enable experiments. Define freezing/boiling points, density. Correct medicine doses. Buying/selling. Farming, engineering, construction, manufacturing. Weight, temperature, length, time vital. Q#4: Why area derived? Ans: Derived quantities combine bases. Area derived as length twice (length × breadth). Area = length × breadth = l × l = l² Length unit m, area m². Q#5: Name four derived units, express as base units. Ans: Newton, pascal, joule, ohm. Derived in bases: Derived QuantitiesDerived UnitsDerived unit in term of base unitVolumeCubic meterm³AccelerationMeter per second squarems⁻²ForceNewton (N)kg ms⁻²PressurePascal (Pa)kg m⁻¹ s⁻² Q#6: Why scientific notation in physics? Ans: Scientific notation simplifies large/small numbers. In physics, expresses extremes easily. N = M × 10^n, M first non-zero, n ±. Example: 150,000,000,000 m = 1.5 × 10¹¹ m. Q#7: What least count? How defined for vernier caliper, screw gauge? Ans: Least Count: Smallest measurable instrument scale value. Vernier Caliper Least Count: Smallest accurate length with vernier. = smallest main division / vernier divisions 1mm main, 10 vernier: 1mm/10 = 0.1mm Screw Gauge Least Count: Smallest accurate with screw gauge. = pitch / circular divisions 0.5mm pitch, 50 divisions: 0.5/50 = 0.01mm Q#8: How find small pebble volume with measuring cylinder? Ans: Half-fill cylinder with water, note V_i. Immerse pebble, note V_f. Pebble volume = V_f - V_i Assignments 1.1 Earth's mass 5,980,000,000,000,000,000,000,000 kg in standard/scientific notation. DATA: Earth mass = 5,980,000,000,000,000,000,000,000 kg FIND: Standard form=? SOLUTION: N = M × 10^n 5,980,000,000,000,000,000,000,000 kg = 5.98 × 10^{24} kg Earth mass in notation 5.98 × 10^{24} kg. 1.2 Seconds in week, power of 10 notation. Data: Seconds in week = ? SOLUTION: Days/week = 7 Hours/day = 24 Min/hour = 60 Sec/min = 60 Week = 7×24×60×60 = 604800 sec Notation: 6.048 × 10^5 sec 1.3 Housefly mass 0.0000214kg in standard notation. DATA: Housefly mass = 0.0000214 kg SOLUTION: N = M × 10^n 0.0000214kg = 2.14 × 10^{-5} kg Housefly mass 2.14 × 10^{-5} kg. 1.4 Bee hummingbird 0.057m in standard, millimeters. DATA: Bee size meter = 0.057m FIND: a. Standard = ? b. Millimeter = ? SOLUTION: a. 0.057 = 5.7 × 10^{-2} m b. 1 m = 10^3 mm Bee size = 5.7 × 10^{-2} × 10^3 mm = 5.7 × 10^1 mm = 57 mm Bee size 57 mm. 1.5 Peshawar-Lahore distance millimeters. DATA: Distance = 489km FIND: Millimeters =? SOLUTION: 489km = 489 × 10^3 m (kilo=10^3) = 489 × 10^3 × 10^3 mm (1m=10^3 mm) = 489 × 10^6 mm = 4.89 × 10^8 mm Distance 4.89 × 10^8 mm. 1.6 Accurate length device: a. Vernier: 1mm main, 50 sliding. b. Screw: 1mm pitch, 25 circular. DATA Vernier main 1mm Vernier divisions 50 Screw pitch 1mm Circular divisions 25 SOLUTION a. Least count = 1mm/50 = 0.02 mm b. Least count = 1mm/25 = 0.04 mm Vernier smaller least count, more accurate. 1.7 200ml water in cm³, m³. DATA: Water volume ml=200ml FIND: cm³=? m³=? SOLUTION: a. 200ml = 200 cm³ (1ml=1cm³) b. 1m³ = 10^6 cm³ 1 cm³ = 10^{-6} m³ 200 cm³ = 200 × 10^{-6} m³ = 2 × 10^{-4} m³ Numerical Questions 1. Prefix to power 10: a. 10^{21} kg mechanical nano-oscillators. 10^{-21} kg = 10^{-21} × 10^3 g = 10^{-18} g = 1 ag b. 3.00 × 10^{18} m neutron star. 3.00 Em c. 149.6 million km Earth-sun. 149.6 × 10^6 km = 149.6 × 10^9 m = 149.6 Gm 2. Angstrom (Å) 10^{-10} m atomic. a. Nanometers in 1.0 angstrom? 1 angstrom = 10^{-10} m = 10^{-1} nm = 0.1 nm b. Femtometers in 1.0 angstrom? 1 angstrom = 10^{-10} m = 10^5 fm = 10^5 fm Wait, correction: 10^{-10} × 10^5 = 10^{-5} for femto 10^{-15}, wait, let's correct as per original calculation. Original has 1.0 × 10^5 angstrom = 10^{-10} fm, but it's 1 angstrom = 10^5 fm Since 10^{-10} m / 10^{-15} m/fm = 10^5 fm Yes. c. Angstroms in 1.0m? 1 m = 10^{10} angstrom 3. Light speed 299,792,458 m/s scientific. a. 2.99792458 × 10^8 m/s b. i. Five sig figs: 2.9979 × 10^8 m/s ii. Three sig figs: 3.00 × 10^8 m/s 4. Power of 10: a. 7 nm = 7 × 10^{-9} m b. 96 MW = 96 × 10^6 W c. 2 GB = 2 × 10^9 B d. 43 pF = 43 × 10^{-12} F e. 2 mm = 2 × 10^{-3} m 5. Standard form: a. Bacterial 0.000000000005 kg = 5 × 10^{-12} kg b. Sun diameter 1,390,000,000 m = 1.39 × 10^9 mAdd to chat1.4sExpertExplain zero error correctionMeasurement error typesmore concise explanations