10th Science Formula Study Material | Physics & Chemistry Sheet

Numericals and chemical equations are often the highest-scoring parts of your exam, provided you have the right formulas at your fingertips. This comprehensive Class 10 Science Formula Study Material compiles every essential mathematical expression, SI unit, and key balance sheet across the syllabus into one organized reference guide. From electricity and light equations to chemical reaction formulas and biological constants, this cheat sheet simplifies your revision, helping you solve complex problems quickly and accurately on exam day.

10^TH SCIENCE FORMULA SHEET (PHYSICS / CHEMISTRY)

UNIT: 1 LAWS OF MOTION

1. Parallel forces acting in the same direction:
F_net = F₁ + F₂

2. Parallel unequal forces acting in opposite directions:
F_net = F₁ - F₂ (if F₁ > F₂)
F_net = F₂ - F₁ (if F₂ > F₁)

3. Parallel equal forces acting in opposite directions:
F_net = F₁ - F₂ = 0 (F₁ = F₂)

4. Linear momentum:
p = mv (m - mass, v - velocity)
SI unit: kg m s^-1 • C.G.S unit: g cm s^-1

5. Torque:
τ = F × d (F - force, d - perpendicular distance)
SI unit: N m • C.G.S unit: dyne cm

6. Moment of couple:
M = F × S (F - force, S - perpendicular distance)
SI unit: N m • C.G.S unit: dyne cm

7. Principle of moments:
F₁ × d₁ = F₂ × d₂
F₁ = (F₂ × d₂) / d₁ | F₂ = (F₁ × d₁) / d₂ | d₁ = (F₂ × d₂) / F₁

8. Change in momentum:
Δp = mv - mu (m - mass, v - final velocity, u - initial velocity)

9. Newton's second law:
F = ma (m - mass, a - acceleration)

SI unit	CGS unit
Newton (N)	dyne
1 N = 1 kg m s^-2	1 dyne = 1 g cm s^-2
1 N = 10⁵ dyne
1 kgf = 1 kg × 9.8 m s^-2 = 9.8 N
1 gf = 1 g × 980 cm s^-2 = 980 dyne

10. Impulse:
J = F × t (F - force, t - time)
SI unit: kg m s^-1 (or) N s
F = Δp / t ⇒ Δp = F × t

11. Universal law of gravitation:
F = (G m₁ m₂) / r² | G = (F r²) / (m₁ m₂)
SI unit of G: N m² kg^-2 • G = 6.674 × 10^-11 N m² kg^-2

12. Weight:
F = W = mg (F - force, W - weight, m - mass, g - acceleration due to gravity)

13. Acceleration due to gravity (g) and Mass of Earth:
mg = (G M m) / r² ⇒ g = GM / r²
SI unit of g: 9.8 m s^-2
M (mass of the Earth) = (g r²) / G = 5.972 × 10²⁴ kg
r (radius of Earth) = 6.37 × 10⁶ m

Apparent Weight in a Lift:

Case	Apparent Weight (R)
Lift moving upwards	R = m(g + a)
Lift moving downwards	R = m(g - a)
Lift at rest	R = mg = W (actual weight)
Lift falling down freely	R = m(g - g) = 0

UNIT: 2 OPTICS

1. Velocity of light:
c = νλ (c - velocity of light = 3 × 10⁸ m s^-1, ν - frequency, λ - wavelength)

2. Snell's law & Refractive index:
sin i / sin r = μ₂ / μ₁
μ = c / v (μ - refractive index, c - speed in vacuum, v - speed in medium)

3. Lens formula:
1/f = 1/v - 1/u (f - focal length, v - image distance, u - object distance)

4. Magnification:
m = v / u = h_i / h_o (h_i - height of image, h_o - height of object)

Magnification	Size	Type of lens
Greater than 1 (m > 1)	Enlarged image	Convex
Equal to 1 (m = 1)	Image same size of the object	Convex
Less than 1 (m < 1)	Image smaller than the object	Concave

5. Lens maker's formula:
1/f = (μ - 1)(1/R₁ - 1/R₂)
(R₁, R₂ - radii of curvature; μ - refractive index of lens material)

6. Power of lens:
P = 1 / f • SI unit: dioptre (1 D = 1 m^-1)
Power of convex lens: Positive | Power of concave lens: Negative

Persistence of vision: Time interval between two consecutive light pulses is less than 1/16 second = 0.0625 s.

7. Myopia (Concave lens):
f = xy / (x - y) (x - person can see up to, y - wants to see up to)

8. Hypermetropia (Convex lens):
f = dD / (d - D) (d - distance of distinct vision, D - near point to be seen)

UNIT: 3 THERMAL PHYSICS

Linear expansion:
ΔL / L₀ = α_L ΔT
ΔL = Change in length (Final - Original); L₀ = Original length; ΔT = Change in temperature; α_L = Coefficient of linear expansion.

Superficial (or) Areal expansion:
ΔA / A₀ = α_A ΔT
ΔA = Change in area; A₀ = Original area; α_A = Coefficient of areal expansion.

Cubical (Volume) expansion:
ΔV / V₀ = α_V ΔT
ΔV = Change in volume; V₀ = Original volume; α_V = Coefficient of cubical expansion.

Gas Laws:
1. Boyle's law: P ∝ 1/V ⇒ PV = Constant
2. Charles's law: V ∝ T ⇒ V / T = Constant
3. Avogadro's law: V ∝ n ⇒ V / n = Constant

UNIT: 4 ELECTRICITY

1. Current & Charge:
I = Q / t (SI unit: Ampere)
Q = ne (n - number of electrons, e - charge of electron = 1.6 × 10^-19 C)
I = ne / t | n = It / e
W = VQ ⇒ V = W / Q (W - work done, V - potential difference, Q - charge)

2. Ohm's law:
V = IR (V - voltage, I - current, R - resistance)

3. Resistance & Resistivity:
R ∝ L, R ∝ 1/A ⇒ R = ρL / A
Resistivity: ρ = RA / L • SI unit: Ω m

4. Conductance & Conductivity:
Conductance: G = 1 / R • SI unit: Ω^-1 (or) mho
Conductivity: σ = 1 / ρ • SI unit: Ω^-1 m^-1 (or) mho m^-1

5. Resistors in Series and Parallel:
Series: R_S = R₁ + R₂ + R₃
Parallel: 1/R_P = 1/R₁ + 1/R₂ + 1/R₃

6. Joule's Law of Heating & Electric Power:
H = W = VQ = VIt = I²Rt
P = W / t = VI = I²R = V² / R

UNIT: 5 ACOUSTICS

1. Wave velocity: v = nλ (n - frequency, λ - wavelength)

2. Effect of density: v ∝ √(1/d) (velocity decreases as density increases)

3. Effect of temperature: v ∝ √T | v_T = (v₀ + 0.61 T) m s^-1

4. Speed of sound: v = d / t

5. Speed of sound in echo method: v = 2d / t

Expression for Apparent Frequency due to Doppler Effect:

(v = speed of sound, v_S = source velocity, v_L = listener velocity, n = true frequency, n' = apparent frequency)

Condition	Apparent Frequency (n')
Both source and listener move towards each other	n' = [(v + v_L) / (v - v_S)] n
Both move away from each other	n' = [(v - v_L) / (v + v_S)] n
Source follows listener	n' = [(v - v_L) / (v - v_S)] n
Listener follows source	n' = [(v + v_L) / (v + v_S)] n
Source at rest, listener moves towards source	n' = [(v + v_L) / v] n
Source at rest, listener moves away from source	n' = [(v - v_L) / v] n
Listener at rest, source moves towards listener	n' = [v / (v - v_S)] n
Listener at rest, source moves away from listener	n' = [v / (v + v_S)] n

UNIT: 6 NUCLEAR PHYSICS

• 1 Curie = 3.7 × 10¹⁰ disintegrations per second

• 1 Rutherford (Rd) = 10⁶ disintegrations per second

• 1 Becquerel (Bq) = 1 disintegration per second

• Mass-energy equivalence: E = mc² (m - mass, c - velocity of light)

UNIT: 7 ATOMS AND MOLECULES

Average atomic mass:
= [(mass of 1st isotope × % abundance) + (mass of 2nd isotope × % abundance)] / 100

Gram molecular mass: Σ (number of atoms × atomic mass of each element)

Formulae for Number of Moles:
• Number of moles = Mass / Atomic mass
• Number of moles = Mass / Molecular mass
• Number of moles = Number of atoms / 6.023 × 10²³
• Number of moles = Number of molecules / 6.023 × 10²³
• Number of moles = Given volume at STP / Molar volume (22.4 L)

Interconversions:
Number of atoms = (Mass × 6.023 × 10²³) / Atomic mass
Number of molecules = (Mass × 6.023 × 10²³) / Molecular mass

Mass % of an element:
Mass % = [Mass of the element in compound / Molecular mass of compound] × 100

UNIT: 9 SOLUTIONS

Solubility:
Solubility = [Mass of solute / Mass of solvent] × 100

Mass percentage:
Mass % = [Mass of solute / Mass of solution] × 100
Mass % = [Mass of solute / (Mass of solute + Mass of solvent)] × 100

Volume percentage:
Volume % = [Volume of solute / Volume of solution] × 100
Volume % = [Volume of solute / (Volume of solute + Volume of solvent)] × 100

UNIT: 10 TYPES OF CHEMICAL REACTIONS

Ionic product of water: K_w = [H⁺][OH^-]
Unit: mol² dm^-6 • At 25°C, value is 1.00 × 10^-14

pH: pH = -log₁₀[H⁺]

pOH: pOH = -log₁₀[OH^-]

Relationship: pH + pOH = 14