Units and Measurement: Comprehensive NEET Physics Notes

1. Introduction

1.1 Physical Quantities and Units

• Physical Quantity: A property of a material or system that can be quantified by measurement.
• Unit: A standard measurement of a physical quantity.
• Fundamental Units: Basic units for length (metre, $m$), mass (kilogram, $kg$), and time (second, $s$), among others.
• Derived Units: Units obtained by combining fundamental units (e.g., velocity, $m{s}^{-1}$).

1.2 The International System of Units (SI)

• SI Units: The globally accepted system of measurement based on seven base units:
• • Length: Metre (m)
  • Mass: Kilogram (kg)
  • Time: Second (s)
  • Electric Current: Ampere (A)
  • Thermodynamic Temperature: Kelvin (K)
  • Amount of Substance: Mole (mol)
  • Luminous Intensity: Candela (cd)

NEET Tip:

Always express answers in SI units during the NEET exam, unless otherwise specified.

2. Significant Figures

2.1 Definition and Rules

• Significant Figures: Digits in a measured quantity that are known with certainty plus one digit that is estimated.
• Rules for Counting Significant Figures:
• • All non-zero digits are significant.
  • Zeros between non-zero digits are significant.
  • Leading zeros are not significant.
  • Trailing zeros are significant if there is a decimal point.

Common Mistake:

Students often mistakenly omit significant trailing zeros in decimal numbers. Always include them when they appear after the decimal point.

2.2 Arithmetic with Significant Figures

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
• Multiplication/Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

3. Dimensions of Physical Quantities

3.1 Dimensional Formulae and Equations

• Dimensional Formula: Expression showing the powers to which the base units are raised to represent a derived unit (e.g., Force: $[ML{T}^{-2}]$).
• Dimensional Equation: An equation representing the relationship between physical quantities using their dimensional formulae.

Did You Know?

Dimensional analysis can be used to check the consistency of physical equations and derive relationships between different physical quantities.

3.2 Applications of Dimensional Analysis

• Checking Dimensional Consistency: Ensure that both sides of an equation have the same dimensions.
• Deriving Relations: Use dimensional analysis to derive relationships between physical quantities.

Real-life Application:

Dimensional analysis is crucial in engineering to ensure that equations and designs are physically valid before testing.

4. Key Formulae and Their Applications

4.1 Formulae Summary

• Volume (V): $V=l\times b\times h$ where $l$, $b$, and $h$ are length, breadth, and height.
• Density ($p$): $\rho =\frac{m}{V}$ where $m$ is mass and $v$ is volume.
• Speed (v): $v=\frac{d}{t}$ where $d$ is distance and $t$ is time.
• Force (F): $F=ma$ where $m$ is mass and $a$ is acceleration.

4.2 Example Problems

1. Problem: Calculate the force on an object of mass 5 kg accelerating at 2 $m{s}^{-2}$.
2. • Solution:
2. Given: $m=5kg$, $a=2$ $m{s}^{-2}$
3. • • Using $F=ma$:
     • $F=5\times 2=10$ $N$
3. Problem: Find the density of an object with mass 100 g and volume 50 cm³.
4. • Solution:
   • • Given: $m=100g=0.1kg$, $V=50c{m}^3=50\times 10^{-6}{m}^3$
     • Using $\rho =\frac{m}{V}$:
     • $\rho =\frac{0.1}{50\times 10^{-6}}=2000kg/m^3$

Common Mistake:

Students sometimes confuse mass with weight. Remember, mass is the amount of matter in an object, while weight is the force exerted by gravity on that mass.

Quick Recap

• SI Units: Ensure all measurements are in SI units.
• Significant Figures: Be precise with significant figures in calculations.
• Dimensional Analysis: Use it to verify equations and derive new formulas.

NEET Exam Strategy

In the NEET exam, understanding the dimensional consistency of an equation can help you quickly eliminate incorrect answer choices. Practice identifying the correct number of significant figures, as this is a common area where marks are lost.

This completes the summary of important formulae and concepts from the chapter on "Units and Measurement."