Important Formulas – Physical Quantities and Measurement

Important Formulas – Physical Quantities and Measurement | Chapter 1 Formula Sheet

Chapter 11: Physical Quantities and Measurement (All Important Formulas)

Introduction

Revise all the Important Formulas for Physical Quantities and Measurement in one place. This comprehensive formula collection includes SI units, SI prefixes, scientific notation, unit conversions, least count, measurement errors, uncertainty, significant figures, dimensional formulas, graphs, and essential Physics equations. Whether you are revising concepts, solving numerical problems, or preparing for examinations, this quick-reference guide helps you recall key formulas efficiently.

📘 Chapter 1: Physical Quantities and Measurement

Formula Sheet (Quick Revision)

This formula sheet contains all the important formulas, SI units, dimensional formulas, conversions, and equations required for quick revision and examination preparation.

1. Physical Quantities

Quantity	SI Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric Current	ampere	A
Temperature	kelvin	K
Amount of Substance	mole	mol
Luminous Intensity	candela	cd

2. SI Prefixes

Prefix	Symbol	Value
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
hecto	h	10²
deca	da	10¹
deci	d	10⁻¹
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²

3. Scientific Notation

N = a \times 10^{n}

where

1 \leq a < 10

4. Unit Conversion

Length

1\,km=10^3\,m

1\,m=10^2\,cm

1 c m = 10 m m

Area

1 m^{2} = 10^{4} c m^{2}

Volume

1\,m^3=10^6\,cm^3

1 L = 10^{- 3} m^{3}

Time

1\,hour=3600\,s

1 m i n u t e = 60 s

5. Least Count

Meter Rule

L C = 1 m m

Vernier Calipers

L C = 0.1 m m

Micrometer Screw Gauge

L C = 0.01 m m

6. Measurement Error

Absolute Error

Δ x = ∣ x_{m e a s u r e d} - x_{t r u e} ∣

Relative Error

\frac{\Delta x}{x}

Percentage Error

% E r r o r = \frac{Δ x}{x} \times 100

7. Measurement Uncertainty

Relative Uncertainty

\frac{Δ x}{x}

Percentage Uncertainty

% U n c e r t a i n t y = \frac{Δ x}{x} \times 100

For Multiplication & Division

\frac{Δ Q}{Q} = \frac{Δ A}{A} + \frac{Δ B}{B}

8. Significant Figures

Addition & Subtraction

Round according to the least number of decimal places.

Multiplication & Division

Round according to the least number of significant figures.

9. Dimensional Formula

Force

[F] = M L T^{- 2}

Work / Energy

[W] = M L^{2} T^{- 2}

Power

[P] = M L^{2} T^{- 3}

Momentum

[p] = M L T^{- 1}

Density

[ρ] = M L^{- 3}

Pressure

[P] = M L^{- 1} T^{- 2}

Gravitational Constant

[G] = M^{- 1} L^{3} T^{- 2}

Planck's Constant

[h] = M L^{2} T^{- 1}

10. Dimensional Homogeneity

A physical equation is correct only if

Dimensions of LHS = Dimensions of RHS

11. Area & Volume

Rectangle

A = l \times w

Square

A = l^{2}

Cube

V = a^{3}

Rectangular Block

V = l \times w \times h

12. Density

ρ = \frac{m}{V}

13. Speed

v = \frac{d}{t}

14. Average Value

\overset{ˉ}{x} = \frac{x_{1} + x_{2} + x_{3} + \dots + x_{n}}{n}

15. Percentage Formula

Percentage= \frac{Part}{Whole}\times100

16. Graph Formula

Slope

m = \frac{Δ y}{Δ x}

Intercept

The point where the graph cuts the x-axis or y-axis.

17. Common Physics Equations (Used in Dimensional Analysis)

Newton's Second Law

F = m a

Work Done

W = F d

Power

P = \frac{W}{t}

Kinetic Energy

K E = \frac{1}{2} m v^{2}

Potential Energy

P E = m g h

Simple Pendulum

T = 2 π \sqrt{\frac{l}{g}}

Gravitational Force

F = \frac{G m_{1} m_{2}}{r^{2}}

Planck's Equation

E = h f

📌 Quick Revision Box

SI Base Units

m, kg, s, A, K, mol, cd

Most Important Dimensional Formulae

Force → $MLT^{-2}$
Work → $ML^2T^{-2}$
Power → $ML^2T^{-3}$
Density → $ML^{-3}$
Pressure → $ML^{-1}T^{-2}$
Momentum → $MLT^{-1}$

Most Important Equations

$\rho=\frac{m}{V}$
$v=\frac{d}{t}$
$F=ma$
$W=Fd$
$P=\frac{W}{t}$
$KE=\frac12 mv^2$
$PE=mgh$
$T=2\pi\sqrt{\frac{l}{g}}$
$E=hf$

💡 Exam Tip

Memorize the SI base units, SI prefixes, dimensional formulas, unit conversions, percentage error, uncertainty formulas, and the commonly used physics equations. These are among the most frequently tested concepts in physics examinations and provide the foundation for solving numerical problems accurately.