Class 11 Physics Chapter 1 Notes : MEASUREMENT OF SMALL QUANTITIES

Complete Notes on Measurement of Small Quantities

Complete Notes on Measurement of Small Quantities

Why Measurement of Small Quantities is Important

Measuring small quantities like length, mass, and time with precision is crucial for CBSE practical exams, NEET, and JEE, using tools like vernier calipers, screw gauges, and simple pendulums.

1. Definition

Measurement of small quantities involves using precise instruments to determine small values of length, mass, or time with high accuracy.

2. Key Formulas

Below are the key formulas for measuring small quantities using common instruments, with units and dimensional formulae:

  • Vernier Caliper (Length):
    • Least Count (LC): LC = 1 MSD - 1 VSD (Main Scale Division - Vernier Scale Division)
    • Measurement: Total Reading = Main Scale Reading + (Vernier Scale Reading × LC)
    • SI Unit: Meter (m)
    • Dimension: [L]
  • Screw Gauge (Length/Diameter):
    • Least Count: LC = Pitch / Number of divisions on circular scale
    • Measurement: Total Reading = Main Scale Reading + (Circular Scale Reading × LC)
    • SI Unit: Meter (m)
    • Dimension: [L]
  • Simple Pendulum (Time):
    • Time Period: T = 2π √(L/g)
    • L: Length of pendulum, g: Acceleration due to gravity (≈9.8 m/s²)
    • SI Unit: Second (s)
    • Dimension: [T]
  • Mass (Balance):
    • Measured using a physical balance or electronic balance.
    • SI Unit: Kilogram (kg)
    • Dimension: [M]

3. Real-Life Example

  • Jewelry Making: A jeweler uses a vernier caliper to measure the diameter of a gemstone (e.g., 2.35 mm) and a screw gauge for the thickness of a gold wire (e.g., 0.12 mm) to ensure precise crafting.

4. Common Exam Questions and Answers

Q1. Calculate the least count of a vernier caliper where 1 MSD = 1 mm and 10 VSD = 9 mm.

Answer:

  • 1 VSD = 9 mm / 10 = 0.9 mm
  • LC = 1 MSD - 1 VSD = 1 mm - 0.9 mm = 0.1 mm or 0.01 cm
Q2. A screw gauge has a pitch of 0.5 mm and 50 divisions on the circular scale. Find its least count.

Answer:

  • LC = Pitch / Number of divisions = 0.5 mm / 50 = 0.01 mm or 0.001 cm
Q3. A simple pendulum has a length of 1 m. Calculate its time period (take g = 9.8 m/s²).

Answer:

  • T = 2π √(L/g)
  • L = 1 m, g = 9.8 m/s²
  • T = 2 × 3.14 × √(1 / 9.8) ≈ 6.28 × √0.102 ≈ 6.28 × 0.32 ≈ 2.01 s

5. Diagram/Table

The table below summarizes the measurement tools for small quantities, their least counts, and applications:

Instrument Quantity Least Count Formula Typical Use
Vernier Caliper Length 1 MSD - 1 VSD Measuring diameter of a cylinder
Screw Gauge Length/Diameter Pitch / No. of divisions Measuring thickness of a wire
Simple Pendulum Time T = 2π √(L/g) Measuring time period
Physical Balance Mass N/A (depends on balance) Measuring mass of small objects

6. Quick Tips/Tricks

  • Vernier Caliper: LC is typically 0.1 mm (1 mm - 0.9 mm); check VSD alignment carefully.
  • Screw Gauge: Memorize LC = Pitch / Divisions; pitch is often 0.5 mm or 1 mm.
  • Simple Pendulum: Use T ≈ 2 s for L = 1 m, g = 9.8 m/s² for quick estimates.
  • NEET/JEE Trick: Always report measurements with significant figures matching the least count.
  • Memorization: “Vernier for length, Screw for thin, Pendulum for time, Balance for mass.”

7. Dimensional Formulae List

Below is a list of dimensional formulae for quantities related to measurement and other key physical quantities, helpful for students:

Quantity Formula SI Unit Dimensional Formula
Length Measured by vernier/screw gauge Meter (m) [L]
Mass Measured by balance Kilogram (kg) [M]
Time T = 2π √(L/g) Second (s) [T]
Force F = ma Newton (N) [M][L][T]-2
Energy W = F·d Joule (J) [M][L]2[T]-2
Acceleration a = v/t m/s² [L][T]-2

Note: Accurate measurement of small quantities using vernier calipers, screw gauges, and simple pendulums is essential for success in physics practicals and numerical problems.

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