PhysicsLaws of Motion
Equations of motion (uniform acceleration)
$v = u + at$; $s = ut + \dfrac{1}{2}at^2$; $v^2 = u^2 + 2as$
Momentum
$p = mv$
Newton's second law
$F = ma = \dfrac{\Delta p}{t}$ (force = rate of change of momentum)
Impulse
$\text{Impulse} = F \times t = \Delta p$
Weight
$W = mg$ (with $g \approx 9.8\ \text{m s}^{-2}$)
Universal law of gravitation
$F = G\dfrac{m_1 m_2}{r^2}$, $G = 6.674 \times 10^{-11}\ \text{N m}^2\,\text{kg}^{-2}$
PhysicsOptics
Mirror formula
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Magnification (mirror)
$m = -\dfrac{v}{u} = \dfrac{h'}{h}$
Relation between f and R
$f = \dfrac{R}{2}$
Lens formula
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
Magnification (lens)
$m = \dfrac{v}{u} = \dfrac{h'}{h}$
Power of a lens
$P = \dfrac{1}{f\ (\text{in metres})}$, unit: dioptre (D)
Refractive index
$n = \dfrac{c}{v} = \dfrac{\sin i}{\sin r}$ (Snell's law)
PhysicsThermal Physics
Heat energy (specific heat)
$Q = mc\,\Delta T$ ($c$ = specific heat capacity)
Latent heat
$Q = mL$ ($L$ = specific latent heat)
Boyle's law (constant T)
$PV = \text{constant}$, so $P_1V_1 = P_2V_2$
Charles's law (constant P)
$\dfrac{V}{T} = \text{constant}$, so $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$
Combined gas equation
$\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}$ (T in kelvin)
PhysicsElectricity
Ohm's law
$V = IR$
Charge and current
$Q = It$
Resistance of a conductor
$R = \rho\dfrac{L}{A}$ ($\rho$ = resistivity)
Resistors in series
$R_s = R_1 + R_2 + R_3 + \cdots$
Resistors in parallel
$\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \cdots$
Electric power
$P = VI = I^2 R = \dfrac{V^2}{R}$
Electrical energy
$E = Pt$; 1 unit $= 1\ \text{kWh} = 3.6 \times 10^6\ \text{J}$
PhysicsAcoustics
Wave relation
$v = f\lambda$ (speed = frequency × wavelength)
Time period and frequency
$f = \dfrac{1}{T}$
Echo / distance of reflector
$2d = v \times t$ ($t$ = time to hear the echo)
SONAR distance
$d = \dfrac{v \times t}{2}$
PhysicsNuclear Physics
Mass–energy equivalence
$E = mc^2$ ($c$ = speed of light $\approx 3 \times 10^8\ \text{m s}^{-1}$)
Half-life
After $n$ half-lives, the remaining quantity $= N_0 \left(\dfrac{1}{2}\right)^{n}$, where $n = \dfrac{\text{total time}}{\text{half-life}}$.
ChemistryMole Concept & Solutions
Number of moles
$n = \dfrac{\text{given mass}}{\text{molar mass}}$
Number of particles
$N = n \times N_A$, $N_A = 6.022 \times 10^{23}$ (Avogadro's number)
Molar volume at STP
$1$ mole of any gas $= 22.4\ \text{litres at STP}$
Percentage by mass
$\%\ \text{mass} = \dfrac{\text{mass of the element}}{\text{molar mass of the compound}} \times 100$
Mass–mole–particles relation
$\text{mass} = n \times \text{molar mass}$; particles $= n \times N_A$
Frequently asked questions
- What are the three equations of motion?
- $v = u + at$, $s = ut + \tfrac{1}{2}at^2$, $v^2 = u^2 + 2as$.
- What is the mirror formula and lens formula?
- Mirror: $\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$; Lens: $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$.
- What is the formula for electric power?
- $P = VI = I^2R = \dfrac{V^2}{R}$, and electrical energy $E = Pt$ (1 unit = 1 kWh).
- How do you find the number of moles?
- $n = \dfrac{\text{given mass}}{\text{molar mass}}$; number of particles $= n \times 6.022\times10^{23}$.
These formulas follow the Tamil Nadu Samacheer Kalvi Class 10 Science textbook. For worked examples and book-back answers, open the full Class 10 Science solutions linked above.