Chapter - 1 : Force
i) Moment of Force = F × r
- Force
- Perpendicular distance
Nature of moment
- Clockwise moment – Negative
- Anticlockwise moment – Positive
ii) Couple or Moment of Couple = F × d
- Either Force
- Couple arm
iii) Principle of Moment: Sum of Anticlockwise Moment = Sum of Clockwise Moment
Chapter - 2 : Work, energy and power
i) Work done = F × S × Cos θ
- F = Force
- S = Displacement
- θ = Angle between F and S
Special Cases
- If the displacement is in the direction of force,i.e.θ =0, then cos 0°= 1; W = F×S
- If the displacement is normal to the direction of force, i.e. θ = 90°, then cos 90°=0; W = 0
- If the displacement is opposite to the direction of force,i.e.θ = 180°, then cos 180°=0; W = -F×S
ii) Work done by Gravity (W) = m × g × h
- m = mass
- a = acceleration due to gravity
- h = height
iii) Power (P) = work (W)\over time (t)
iv) Power (P) = Force (F) × Velocity (v)
v) Potential Energy: Ep= m × g × h
- m = mass
- a = acceleration due to gravity
- h = height
vi) Kinetic Energy: Ek = 1\over 2 × m × v2
- m = mass
- v = velocity
vii) Momentum (p) = \sqrt{2 \times m \times K}
(viii) Work-energy theorem: Work (W) = 1\over 2(v2 – u2)
- m =mass
- u =initial velocity
- v = final velocity
Chapter - 3 : Machine
i) Mechanical Advantage (MA) = Load (L) \over Effort (E)
ii) Velocity Ratio (VR) = velocity\ of\ effort\ (v_E) \over velocity\ of\ Load\ (v_L)
iii) Velocity Ratio (VR) = Displacement\ of\ effort\ (d_E) \over Displacement\ of\ Load\ (d_L)
iv) Principle of a Machine:
- For ideal Machine – Work Input =Work Output
- For Real Machine -Work Input >Work Output
v) Mechanical Advantage (M.A) =Velocity Ratio(V.R) × Efficiency(n)
vi) Load × Load Arm =Effort × Effort Arm
vii) Mechanical Advantage (M.A) = Effort\ arm \over Load\ arm
Note :
- For Class – I Lever: M.A. and V.R. can have any value.
- For Class – II Lever: M.A and V.R > 1 (always)
- For Class – III Lever: M.A and V.R < 1(always)
Pulley
vii) Single Fixed Pulley
- Mechanical Advantage =1
- Velocity Ratio = 1
- Efficiency (η)=1 or 100%
ix) Single Movable Fulley
- Mechanical Advantage = 2
- Velocity Ratio = 2
- Efficiency (η) =1 or 100%
x) One fixed pulley and other movable pulleys
- Mechanical Advantage = 2n (where n = no of movable pulley)
- Velocity Ratio = 2n (where n = no of movable pulley)
- Efficiency (η) = 1 or 100%
xi) Block and tackle system
- Mechanical Advantage =n (where n = no of pulley)
- Velocity Ratio = n (where n = no of pulley )
- Efficiency (η) = 1 or 100%
xii) Effect of weight of pulley on M.A, V.R and n
- Mechanical Advantage = n – w/E
- Velocity Ratio = n
- Efficiency (η) = 1 – w/nE
Chapter - 4 : Refraction of Light at Plane Surface
Refractive Index (RI)
i) RI (μ) = sin\ i\over sin\ r
ii) RI (μ) = velocity\ of\ light\ in\ vacuum\over velocity\ of\ light\ in\ medium
iii) Relative RI (1μ2) = velocity\ of\ light\ in\ medium\ 1 \over velocity\ of\ light\ in\ medium\ 2
iv) Relative RI (1μ2) = μ_2\over μ_1
v) Velocity (V) = f × λ
- f = frequency
- λ = wavelength
vi) Principal of reversibility: 1μ2 × 2μ1 = 1
Prism
i) Deviation (δ) = (i1 + i2)-(r1 + r2)
ii) r1+r₂=A
iii) Minimum Deviation (δmin) = 2i – A
- Angle of incidence =i1
- Angle of emergence =i2
- Angle of prism = A
- Angle of refraction at first surface =r1
- Angle of refraction at first surface =r2
Real and Apparent Depth
i) Refractive Index (1μ2) = Real\ depth\over Apparent\ depth
ii) shift = Real Depth (1 – 1\over 1μ_2)
iii) Critical angle (C) : 1μ2 = 1 / sin C
Chapter - 5 : Refraction Through A Lens
Images formed by convex lens:
| Position of the object | At infinity |
 | |
| Position of image | At F2 |
| Size | Highly Diminished |
| Nature | Real and Inverted |
| Position of the object | Beyond 2F1 |
 | |
| Position of image | Between F2 and 2F2 |
| Size | Diminished |
| Nature | Real and Inverted |
| Position of the object | At 2F1 |
 | |
| Position of image | At F2 |
| Size | Same size |
| Nature | Real and Inverted |
| Position of the object | Between F1 and 2F1 |
 | |
| Position of image | Beyond F2 |
| Size | Magnified |
| Nature | Real and Inverted |
| Position of the object | At F1 |
 | |
| Position of image | At infinity |
| Size | Highly Magnified |
| Nature | Real and Inverted |
| Position of the object | Between F1 and O |
 | |
| Position of image | On the same side of the lens as the object |
| Size | Magnified |
| Nature | Virtual and erect |
Images formed by concave lens:
| Position of the object | At Infinity |
 | |
| Position of image | At the focus, F2 |
| Size | Highly diminished |
| Nature | Virtual and erect |
| Position of the object | Anywhere in front of lens |
 | |
| Position of image | At the focus, F2 |
| Size | Highly diminished |
| Nature | Virtual and erect |
iii) Lens Formula: {1\over v} – {1\over u} = {1\over f}
- u = object distance from the lens
- v = image distance from the lens
- f = focal length
iv) Linear Magnification (m) :
- m = size\ of\ image\over size\ of\ object
- m = Distance\ of\ image\ from\ the\ lens\over Distance\ of\ object\ from\ the\ lens
v) Power of Lens: P = 1\over f\ (in\ m)
- Concave lens : – ve power
- Convex lens : + ve power
Chapter - 7 : Sound
i) Relation Between time period and frequency of wave:
(a) Time Period (T) = 1/Frequency (f)
(b) Frequency (f) = 1/Time Period (T)
ii) Relation between velocity, frequency and wavelength of wave:
Velocity (v) = frequency (f) × wavelength (λ)
iii) Echo of sound:
Depth of sea = velocity × time\over 2
iv) Height = t \sqrt{V^2-v^2}\over 2
Where
- V = Velocity of sound in air
- v = velocity of aeroplane
- t = time difference between sound and its echo
Chapter - 8 : Current Electricity
i) Electric potential difference:
(a) If ‘W’work is done to bring Q coulomb of positive charge from infinity to a particular point in an electric field,then the potential at that point,
V = W/Q
or, W = V.Q
(b) If W joule of work is done to move a coulomb of charge from a point A to another point B, then the difference between A and B,
VA-VB=W/Q
ii) Electro-Motive Force (EMF):
If W work is done to move Q charge around a complete circuit, then EMF of the cell,
EMF =W/Q
iii) Electric current :
If a charge Q flows through a cross-section of a conductor in t seconds, then the magnitude of current,
I=Q/t
iv) Ohm’s law:
If the current flowing through the conductor is I when the potential difference across its two ends is V, then according to Ohm’s law, V =I.R where R is the resistance of the conductor.
v) EMF and internal resistance of a cell:
When I current is flowing through a closed circuit driven by a cell having emf E and internal resistance r, then terminal potential difference across the cell is given by, V =E – I.r, where I.r is known as lost volt.
vi) Resistance of a conductor:
Resistance (R) = ρ(l/a)
- l = length
- a = cross-section
- ρ = resistivity or specific resistance
vii) Conductivity :
σ = 1/ρ = l/Ra
- l = length
- a = cross-section
- ρ = resistivity or specific resistance
viii) Resistances connected in series :
When resistances R1, R2, and R3 are joined in series, the equivalent resistance,
R=R₁+R₂+R₃
ix) Resistances connected in parallel:
For a number of resistances like R1, R2, and R3 connected parallel, the equivalent resistance,
1/R = 1/R1 + 1/R2 + 1/R3
x) Cells in series
I = nE\over R + nr
- n = Number of cells
- R = External resistance
- E = Emf cell
- r = Internal resistance
xi) Cells in parallel
I = nE\over nR + r
- n = Number of cells
- R = External resistance
- E = Emf cell
- r = Internal resistance
xii) Joule’s Law of heating
H = I2Rt
- H = Heat Produced
- I = Current
- R = Resistance
- t = time
xiii) Electrical Energy
(a) Work = Vit
(b) Work = I2Rt
(c) Work = {V^2\over R}t
xiv) Electrical Power
(a) Power = Work\over time
(b) Power = VIt\over t = VI
Chapter - 11 : Calorimetry
i) Fundamental principle of calorimetry
Heat lost by hot body = heat gained by cold body
ii) Heat necessary to raise the temperature of a body
Heat (Q) = m × s × Δt
Where
- m = mass of body
- s = specific heat of material
- Δt = change in temperature
iii) Thermal capacity:
- Formula: Thermal capacity (C) = mass (m) × Sp heat (s)
- unit: cal/ºC or J/K
iv) Latent Heat:
Heat (Q) = mass (m) × Latent Heat (L)
Chapter - 12 : Calorimetry
i) Radioactive transformations:
There are three types of radioactive transformation –
(a) α decay: zXA → z-2YA-4 + 2He4 (α-particle)
(b) β decay: zXA → z+1YA + -1βo (β-particle)
(c) γ decay: zXA → zXA + γ
ii) Mass defect
For a nuclide zXA, the mass defect
Δm = Z.mp + (A – Z).mn – MN
- mp = mass of proton
- mn = mass of neutron
- MN = mass of the nucleus
- A = Mass number
- Z = Atomic Number
Binding energy
(a) According to mass-energy equivalence, Binding energy,
ΔE = Δm. c2 = [Z.mp + (A – Z)mn MN]. c2
(b) 1 MeV = 1.6 × 10-13 J
(c) For 1 amu mass defect, binding energy E = 931 MeV.
Binding energy per nucleon:
B/A = Total\ binding\ energy\over Number\ of\ nucleon