Measurement of Physical Quantities & Density

A physical quantity is any measurable property of an object or phenomenon. • Fundamental (Basic) Quantities: These are basic physical quantities that do not depend on any other quantities for their definition: 1. Length: The distance between two points. SI unit is the Metre (m). Measured using metre rules, measuring tapes, vernier callipers, and micrometer screw gauges. 2. Mass: The quantity of matter contained in a body. SI unit is the Kilogram (kg). Measured using beam balances, lever balances, or electronic top-pan balances. 3. Time: The interval between two events. SI unit is the Second (s). Measured using stopwatches and digital timers. 4. Temperature: The degree of hotness or coldness of a body. SI unit is the Kelvin (K), though Degree Celsius (°C) is widely used. Measured with mercury or alcohol thermometers. 5. Electric Current: The rate of flow of electric charges. SI unit is the Ampere (A). Measured with an ammeter. • Derived Quantities: Quantities obtained by combining fundamental quantities through multiplication or division: - Area = Length × Width (m² or cm²) - Volume = Length × Width × Height (m³ or cm³) - Speed = Distance ÷ Time (m/s) - Density = Mass ÷ Volume (kg/m³ or g/cm³) - Force = Mass × Acceleration (Newton, N = kg·m/s²)

Accurate scientific measurements require avoiding observational errors: • Parallax Error: This is the apparent shift in the position of an object or meniscus when viewed from different angles. To avoid parallax error: - Always position your eye directly perpendicular (at a right angle, 90°) to the scale reading. - When measuring liquids in a measuring cylinder, read the BOTTOM of the concave meniscus for water and aqueous solutions (or the TOP of the convex meniscus for mercury). • Measuring Volume of Regular vs Irregular Solids: - Regular Solids (Geometric formulas): * Cuboid / Rectangular block: Volume = length × width × height. * Cylinder: Volume = π × r² × h. * Sphere: Volume = 4/3 × π × r³. - Irregular Solids (Water displacement method): * For an insoluble irregular stone: Fill a measuring cylinder with an initial volume of water (V₁). * Gently lower the stone tied to a thin thread into the water until completely submerged. * Record the new elevated volume (V₂). * Volume of stone = V₂ - V₁. * If the object is too large for a measuring cylinder, use a Eureka (displacement/overflow) can filled to the spout. The overflow water collected in a measuring cylinder equals the volume of the submerged solid.

Density is defined as the mass per unit volume of a substance. It measures how tightly matter is packed together. • Density Formula: Density (ρ) = Mass (m) / Volume (V) - SI unit: Kilograms per cubic metre (kg/m³) - Laboratory unit: Grams per cubic centimetre (g/cm³) - Conversion: 1 g/cm³ = 1,000 kg/m³. • Density of Pure Water: Pure liquid water at 4°C has a density of exactly 1.0 g/cm³ (or 1,000 kg/m³). • Sinking and Floating: - An object will FLOAT in a fluid if its average density is LESS than the density of the fluid. - An object will SINK in a fluid if its average density is GREATER than the density of the fluid. - A block of dry wood (density ~0.7 g/cm³) floats on water, whereas an iron nail (density 7.8 g/cm³) sinks immediately. - Massive steel ocean cargo ships float because their hollow interior contains huge volumes of air, reducing their overall average density to far less than 1.0 g/cm³!