Madhyamik Class 9 Physical Science Formula
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System of Measurement and Measuring Devices
UNIT OF LENGTH:
| Unit Name | Symbol | Equivalent in Meters | Conversions |
|---|---|---|---|
| Fermi | fm | 10-15 m | 1 fm = 10-15 m |
| Angstrom | Å | 10-10 m | 1 Å = 105 fm |
| Nanometer | nm | 10-9 m | 1 nm = 10 Å |
| Micrometer | µm | 10-6 m | 1 µm = 1000 nm |
| Millimeter | mm | 10-3 m | 1 mm = 1000 µm |
| Centimeter | cm | 10-2 m | 1 cm = 10 mm |
| Meter | m | 1 m | 1 m = 100 cm |
| Kilometer | km | 103 m | 1 km = 1000 m |
| Astronomical Unit | AU | 1.496 × 1011 m | 1 AU = 1.496 × 108 km |
| Light Year | ly | 9.461 × 1015 m | 9.461 × 1012 km |
| Parsec | pc | 3.086 × 1016 m | 1 pc = 3.26 ly |
UNIT OF MASS:
- 1 metric ton (MT) = 10 quintal (q) = 10³ kg = 10⁶ g = 10⁹ mg
- 1 amu = mass of 1 atom of C¹²
UNIT OF TIME:
| Name | Symbol | In Seconds (s) | Conversions |
|---|---|---|---|
| Millisecond | ms | 10-3 s | 1 ms = 0.001 s |
| Second | s | 1 s | 1 min = 60 s |
| Minute | min | 60 s | 1 hr = 60 min |
| Hour | hr | 3600 s | 1 day = 24 hr |
| Day | d | 86,400 s | 1 week = 7 days |
| Week | wk | 604,800 s | 1 month ≈ 4.3 weeks |
| Month | mo | 2.63 × 106 s | 1 year = 12 months |
| Year | yr | 3.154 × 107 s | 1 decade = 10 years |
| Decade | – | 3.154 × 108 s | 1 century = 10 decades |
| Century | – | 3.154 × 109 s | 1 millennium = 10 centuries |
| Millennium | – | 3.154 × 1010 s | 1 millennium = 1000 1000 years |
UNIT OF VOLUME:
| Unit Name | Symbol | In Cubic Meters (m³) | Conversions |
|---|---|---|---|
| Cubic Centimeter | cm³ | 10−6 m3 | 1 cm3 = 1 mL |
| Milliliter | mL | 10−6 m3 | mL = 11 cm3 |
| Cubic Decimeter | dm³ | 10−3 m3 | 1 dm3 = 1000 cm3 = 1 L |
| Liter | L | 10−3 m3 | 1 L = 1000 mL = 1 dm3 |
UNIT OF DENSITY:
- Density = mass / volume
- g/cc or g/cm³ or kg/m³ or kgm⁻³
MEASUREMENT OF MASS USING COMMON BALANCE
(i) Unequal arm length but same scale pan weight:
Mass on left pan × Length of left arm = Mass on right pan × Length of right arm
(ii) Equal arm length but unequal scale pan weight:
True weight, W = (W₁ + W₂) / 2,
where W₁ and W₂ are counterpoise weights in two scale pans.
(iii) Unequal arm lengths and unequal scale pan weights:
True weight, W = √(W₁ × W₂),
where W₁ and W₂ are counterpoise weights in two scale pans.
ERROR CALCULATION
(i) Absolute error = | True value – Measured value |
(ii) Relative error = \text{absolute error}\over \text{measured value}
(iii) Percentage error = Relative error × 100 %
Force and Motion
Distance
- Formula: Distance = Speed × time
- Unit: metre (m) in SI and cm in CGS
- It is a scalar quantity.
Speed
- Formula: Speed = \text {Distance}\over \text { time}
- Avg Speed = \text {Total Distance}\over \text {Total time}
- Unit: metre/second (m/s) in SI and cm/s in CGS
- It is a scalar quantity.
Displacement
- Formula: Displacement = velocity × time
- Unit: metre (m) in SI and cm in CGS
- It is a vector quantity.
Velocity
- Formula: Velocity = \text {Displacement}\over \text { time}
- Avg Velocity = \text {Total Displacement}\over \text {Total time}
- Unit: metre/second (m/s) in SI and cm/s in CGS
- It is a vector quantity.
Acceleration
- Formula: Acceleration = \text{v – u}\over \text{t}
- Unit: metre/second2 (m/s2) in SI and cm/s2 in CGS
- It is a vector quantity
Equation of Motion
- v = u + at
- s = ut + 1/2 at2
- v2 = u2 + 2as
- u = initial velocity
- v = Final velocity
- a = acceleration
- s = displacement
- t = time
Law of parallelogram of forces
The magnitude and direction of the resultant R is given by:
(a) R = P + Q and is parallel to P and Q when θ = 0°.
(b) R = |P – Q| and is directed along the larger of the two forces when θ = 180°.
(c) R = √(P² + Q²) and is directed along the diagonal of the rectangle having P and Q as adjacent sides, i.e. θ = 90°.
Momentum
(i) Momentum (p) = Mass (m) × velocity (v)
(ii) Initial momentum = Mass (m) × Initial velocity (u)
(iii) Final momentum = Mass (m) × Final velocity (v)
(iv) Change of momentum (Δp) = m (v – u)
(v) Rate of Change of momentum = m (v – u)/t
Force
(i) Force (F) = mass (m) × acceleration (a)
(ii) Force (F) = m (v – u)/t
Recoil velocity of gun (V) = – \text {m}\ over \text {M} v
- m = mass of bullet
- v = mass of velocity
- M = Mass of gun
Pressure of liquid and Air
(i) Thrust (F) = Pressure (P) × Area (A)
(ii) Liquid Pressure (P) = h × d × g
- h = depth of the point
- d = density of liquid
- g = acceleration due to gravity
(iii) Atmospheric pressure (PA) = h × dHg × g
- h = height of mercury column
- dHg = density of mercury
- g = acceleration due to gravity
(iv) Upthrust (F) = V × d × g
- V = volume of solid body
- d = density of liquid in which the solid body is immersed
- M = Vd = mass of liquid having same volume as the solid body
- W = weight of the displaced liquid
(v) Density (d) = \text {Mass} \over \text {volume}
(vi) Relative density (RD) = \text {Weight of the substance} \over \text {weight of an equal volume of water at 4ºC}
(vii) Bernoulli’s theorem : In a steady flow, the sum of all forms of energy in a fluid is the same at all points that are free of viscous forces.
potential energy + kinetic energy + pressure energy = constant
hg + 1/2V2 + p/d = constant
(viii) Stress (S) = Force/Area
(ix) Young’s Modulus (Y) = \text {Longitudinal stress} \over \text {Longitudinal strain} = {\text {F} \over \text {A}} × {\text {L} \over \text {ΔL}}
where
- L = original length
- ΔL = change in length
Atomic Structure, the Physical and Chemical Properties of Matter
Atomic structure
An element X having mass number A and atomic number Z is symbolically represented as or ZXA.
(i) Number of proton = A
(ii) Number of electron = A
(iii) Number of Neutron = A – Z
Concept of Mole
(i) Number of moles = \text{Given mass}\over \text{Molecular mass}
(ii) Number of moles = \text{Given Volume}\over \text{22.4}
(iii) Number of moles = \text{Number of particles}\over 6.022 × 10^23
Solution
Solubility = \text{weight of solute (in g)}\over \text{weight of solvent (in g)} × 100
Work, Power, Energy
(i) Work (W) = Force (F) × displacement (d)
(ii) Power
(a) Power (P) = Work/time
(b) Power (P) = Force (F) × velocity (v)
(iii) Potential Energy (Ep) = m × g × h
- m = mass of the body
- g = acceleration due to gravity
- h = height above the ground
(iv) Kinetic energy (Ek) = 1\over2 mv2
(v) Work (W) = 1\over2 mv2 – 1\over2 mu2
Heat
Fundamental principle of calorimetry :
(i) Heat lost by hot bodies = Heat gained by cold bodies
(ii) m1 × s1 × (t1 – t) = m2 × s2 × (t – t2)
Heat necessary to raise the temperature of a body:
(ii) Heat (Q) = m × s × t
Where,
- m = mass of body
- s = specific heat of material
- t = change in temperature
(iii) Thermal capacity :
(a) Formula : C = m s
(b) Unit : cal/ °C or J/K
(iv) Work (W) = Joule constant (J) × Heat (H)
(v) Heat (Q) = mass (m) × Specific Latent heat (L)
Sound
(i) Relation between time period and frequency of wave :
(a) Time Period (T) = 1\over \text{frequency (f)}
(b) Frequency (f) = 1\over \text{Time Period (T)}
(ii) Velocity (v) = frequency (f) × wavelength (λ)
(iii) Depth of sea = \text{velocity × time}\over 2
(iv) Height (H) = \text{t√(V2 – v2)}\over 2
Where
- V = Velocity of sound in air
- v = velocity of aeroplane
- t = time difference between sound and its echo