PhysicsMeasurement
Density
$\rho = \dfrac{\text{mass}}{\text{volume}} = \dfrac{m}{V}$; SI unit $\text{kg/m}^3$.
Relative density
$\text{RD} = \dfrac{\text{density of substance}}{\text{density of water}}$ (no unit).
SI base units
length — metre (m), mass — kilogram (kg), time — second (s).
Least count
The smallest measurement an instrument can read; e.g. for a vernier caliper $=$ 1 main-scale division $-$ 1 vernier-scale division.
PhysicsMotion
Speed and velocity
Speed $= \dfrac{\text{distance}}{\text{time}}$; velocity $= \dfrac{\text{displacement}}{\text{time}}$.
Acceleration
$a = \dfrac{v - u}{t}$; SI unit $\text{m/s}^2$.
Equations of motion
$v = u + at$; $s = ut + \dfrac{1}{2}at^2$; $v^2 = u^2 + 2as$.
Momentum
$p = mv$; SI unit $\text{kg m/s}$.
PhysicsFluids
Pressure
$P = \dfrac{F}{A}$; SI unit pascal (Pa) $= \text{N/m}^2$.
Pressure in a liquid
$P = h\rho g$, where $h$ is depth, $\rho$ density and $g$ acceleration due to gravity.
Pascal's law
Pressure applied to an enclosed fluid is transmitted equally in all directions.
Archimedes' principle
The upward buoyant force on an immersed body equals the weight of the fluid it displaces.
PhysicsElectric Charge and Electric Current
Electric current
$I = \dfrac{Q}{t}$; SI unit ampere (A).
Ohm's law
$V = IR$; resistance $R$ in ohm ($\Omega$).
Resistance of a conductor
$R = \rho\dfrac{l}{A}$, where $\rho$ is resistivity, $l$ length and $A$ area of cross-section.
Electric power
$P = VI = I^2R = \dfrac{V^2}{R}$; SI unit watt (W).
Resistors in series / parallel
Series: $R = R_1 + R_2 + \dots$; Parallel: $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$
PhysicsLight
Laws of reflection
Angle of incidence $=$ angle of reflection; the incident ray, reflected ray and normal lie in one plane.
Refractive index
$n = \dfrac{c}{v} = \dfrac{\sin i}{\sin r}$ (Snell's law), where $c$ is the speed of light in vacuum and $v$ in the medium.
Real vs virtual image
A real image can be caught on a screen; a virtual image cannot.
PhysicsHeat
Heat energy
$Q = mc\,\Delta T$, where $m$ is mass, $c$ specific heat capacity and $\Delta T$ temperature change.
Specific heat capacity
Heat to raise 1 kg by 1 K; SI unit $\text{J kg}^{-1}\text{K}^{-1}$.
Latent heat
$Q = mL$ during a change of state (no temperature change); $L$ is the latent heat.
Modes of heat transfer
Conduction (through solids), convection (through fluids) and radiation (no medium needed).
PhysicsSound
Wave relation
$v = f\lambda$, where $v$ is speed, $f$ frequency and $\lambda$ wavelength.
Time period
$T = \dfrac{1}{f}$.
Echo
$2d = v\times t$, where $d$ is the distance to the reflecting surface; the reflected sound must arrive at least $0.1$ s after the original.
Audible range
About $20$ Hz to $20{,}000$ Hz for humans.
ChemistryAtomic Structure
Atomic number and mass number
Atomic number $Z =$ number of protons; mass number $A =$ protons $+$ neutrons. Number of neutrons $= A - Z$.
Electrons per shell
Maximum electrons in a shell $= 2n^2$ ($n = 1,2,3,\dots$): 2, 8, 18, 32.
Isotopes and isobars
Isotopes: same $Z$, different $A$. Isobars: same $A$, different $Z$.
ChemistryAcids, Bases and Salts
The pH scale
Ranges from $0$ to $14$: pH $< 7$ acidic, pH $= 7$ neutral, pH $> 7$ basic.
Neutralisation
Acid $+$ Base $\rightarrow$ Salt $+$ Water. e.g. $\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$.
Acids and bases
An acid releases $\text{H}^+$ ions in water (turns blue litmus red); a base releases $\text{OH}^-$ ions (turns red litmus blue).
Frequently asked questions
- What are the three equations of motion?
- $v = u + at$, $s = ut + \dfrac{1}{2}at^2$, $v^2 = u^2 + 2as$ (for uniform acceleration).
- What is Ohm's law and electric power?
- $V = IR$; power $P = VI = I^2R = \dfrac{V^2}{R}$ (in watts).
- What is the formula for pressure in a liquid?
- $P = \dfrac{F}{A}$; at depth $h$ in a liquid, $P = h\rho g$.
- What is the relation between speed, frequency and wavelength?
- $v = f\lambda$; the human audible range is about $20$ Hz to $20{,}000$ Hz.
These formulas follow the Tamil Nadu Samacheer Kalvi Class 9 Science textbook. For worked examples and book-back answers, open each chapter's full solutions linked above.