i) Moment of Force = F × r
Nature of moment
ii) Couple or Moment of Couple = F × d
iii) Principle of Moment: Sum of Anticlockwise Moment = Sum of Clockwise Moment
i) Work done = F × S × Cos θ
Special Cases
ii) Work done by Gravity (W) = m × g × h
iii) Power (P) = work (W)\over time (t)
iv) Power (P) = Force (F) × Velocity (v)
v) Potential Energy: Ep= m × g × h
vi) Kinetic Energy: Ek = 1\over 2 × m × v2
vii) Momentum (p) = \sqrt{2 \times m \times K}
(viii) Work-energy theorem: Work (W) = 1\over 2(v2 – u2)
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:
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 :
Pulley
vii) Single Fixed Pulley
ix) Single Movable Fulley
x) One fixed pulley and other movable pulleys
xi) Block and tackle system
xii) Effect of weight of pulley on M.A, V.R and n
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
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
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
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}
iv) Linear Magnification (m) :
v) Power of Lens: P = 1\over f\ (in\ m)
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
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)
vii) Conductivity :
σ = 1/ρ = l/Ra
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
xi) Cells in parallel
I = nE\over nR + r
xii) Joule’s Law of heating
H = I2Rt
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
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
iii) Thermal capacity:
iv) Latent Heat:
Heat (Q) = mass (m) × Latent Heat (L)
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
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
