Chapter 1 Solved Numericals: Physical Quantities and Measurement

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Chapter Overview & SLOs

What is covered in these solved numericals? This section provides comprehensive step-by-step solutions to the numerical problems for Chapter 1, "Physical Quantities and Measurement." The exercises focus on the practical application of mathematical tools in physics. How do we convert numbers into scientific notation and use prefixes? You will learn to convert standard values into scientific notation (expressing numbers as a × 10ⁿ where 1 ≤ a < 10) and use prefixes like nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), centi (10⁻²), kilo (10³), mega (10⁶), and giga (10⁹) to express very large or small measurements efficiently. How do we perform multi-step unit conversions? You will find detailed solutions for complex unit conversions, including: - Calculating a person's age in seconds, milliseconds, and megaseconds - Converting micrometers (µm) to kilometers (km) - Converting between different units of length, mass, and time How do we calculate least count for measuring instruments? A significant portion of these numericals is dedicated to precision instruments: - Vernier Calipers Least Count: Least Count = 1 MSD - 1 VSD = (Main scale smallest division) / (Number of Vernier scale divisions). Typical value: 0.1 mm or 0.01 cm. - Screw Gauge Least Count: Least Count = Pitch / Total divisions on circular scale. Typical value: 0.01 mm or 0.001 cm. How do we calculate total readings from instrument diagrams? You will learn to determine total readings from instrument diagrams by: - Identifying main scale reading (MSR) - Identifying coinciding division on Vernier scale (VSD) or circular scale (CSD) - Total Reading = MSR + (VSD × Least Count) for Vernier calipers - Total Reading = MSR + (CSD × Least Count) for screw gauge - Accounting for zero error correction (positive or negative zero error) These solutions are strictly designed to help students master the mathematical requirements of the FBISE 2026 annual examination.

• How do we convert physical quantities into scientific notation and use prefixes? Convert large and small physical quantities into scientific notation (a × 10ⁿ where 1 ≤ a < 10) and express measurements using appropriate SI prefixes including nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), centi (10⁻²), kilo (10³), mega (10⁶), and giga (10⁹).
• How do we perform multi-step unit conversions? Perform multi-step unit conversions for time (years to seconds, milliseconds, megaseconds) and length (micrometers to kilometers, millimeters to meters) using dimensional analysis and conversion factors.
• How do we calculate the least count of measuring instruments? Apply the least count formulas for Vernier calipers (Least Count = 1 MSD - 1 VSD = Main scale division / Number of Vernier divisions) and screw gauges (Least Count = Pitch / Total divisions on circular scale) with typical values of 0.1 mm and 0.01 mm respectively.
• How do we calculate total readings from instrument diagrams? Analyze instrument diagrams to calculate total measurements using the formula Total Reading = Main Scale Reading + (Coinciding Division × Least Count), accounting for zero error correction (positive zero error subtract, negative zero error add), and correctly identify the coinciding division on Vernier scale and circular scale.

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