Table of Contents

Toggle## 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: E_{p}= m × g × h

- m = mass
- a = acceleration due to gravity
- h = height

vi) Kinetic Energy: E_{k }= 1\over 2 × m × v^{2}

- m = mass
- v = velocity

vii) Momentum (p) = \sqrt{2 \times m \times K}

(viii) **Work-energy theorem: **Work (W) = 1\over 2(v^{2} – u^{2})

- 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 (_{1}μ_{2}) = velocity\ of\ light\ in\ medium\ 1 \over velocity\ of\ light\ in\ medium\ 2

iv) Relative RI (_{1}μ_{2}) = μ_2\over μ_1

v) Velocity (V) = f × λ

- f = frequency
- λ = wavelength

vi) **Principal of reversibility:** _{1}μ_{2} × _{2}μ_{1} = 1

**Prism**

i) Deviation (δ) = (i_{1} + i_{2})-(r_{1} + r_{2})

ii) r_{1}+r_{₂}=A

iii) Minimum Deviation (δ_{min}) = 2i – A

- Angle of incidence =i
_{1} - Angle of emergence =i
_{2} - Angle of prism = A
- Angle of refraction at first surface =r
_{1} - Angle of refraction at first surface =r
_{2}

**Real and Apparent Depth**

i) Refractive Index (_{1}μ_{2}) = Real\ depth\over Apparent\ depth

ii) shift = Real Depth (1 – 1\over 1μ_2)

iii) **Critical angle (C) :** _{1}μ_{2} = 1 / sin C

## Chapter - 5 : Refraction Through A Lens

**Images formed by convex lens:**

Position of the object | At infinity |

Position of image | At F_{2} |

Size | Highly Diminished |

Nature | Real and Inverted |

Position of the object | Beyond 2F_{1} |

Position of image | Between F_{2} and 2F_{2} |

Size | Diminished |

Nature | Real and Inverted |

Position of the object | At 2F_{1} |

Position of image | At F_{2} |

Size | Same size |

Nature | Real and Inverted |

Position of the object | Between F_{1} and 2F_{1} |

Position of image | Beyond F_{2} |

Size | Magnified |

Nature | Real and Inverted |

Position of the object | At F_{1} |

Position of image | At infinity |

Size | Highly Magnified |

Nature | Real and Inverted |

Position of the object | Between F_{1} 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, F_{2} |

Size | Highly diminished |

Nature | Virtual and erect |

Position of the object | Anywhere in front of lens |

Position of image | At the focus, F_{2} |

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,

V_{A}-V_{B}=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 R_{1}, R_{2}, and R_{3} are joined in series, the equivalent resistance,

R=R_{₁}+R_{₂}+R_{₃}

**ix) Resistances connected in parallel:**

For a number of resistances like R_{1}, R_{2}, and R_{3} connected parallel, the equivalent resistance,

1/R = 1/R_{1} + 1/R_{2} + 1/R_{3}

**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 = I^{2}Rt

- H = Heat Produced
- I = Current
- R = Resistance
- t = time

**xiii) Electrical Energy**

(a) Work = Vit

(b) Work = I^{2}Rt

(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: _{z}X^{A} → _{z-2}Y^{A-4} + _{2}He^{4} (α-particle)

(b) β decay: _{z}X^{A} → _{z+1}Y^{A} + _{-1}β^{o} (β-particle)

(c) γ decay: _{z}X^{A} → _{z}X^{A} + γ

**ii) Mass defect**

For a nuclide _{z}X^{A}, the mass defect

Δm = Z.m_{p} + (A – Z).m_{n} – M_{N}

- m
_{p}= mass of proton - m
_{n}= mass of neutron - M
_{N}= mass of the nucleus - A = Mass number
- Z = Atomic Number

**Binding energy**

(a) According to mass-energy equivalence, Binding energy,

ΔE = Δm. c^{2} = [Z.m_{p} + (A – Z)m_{n} M_{N}]. c^{2}

(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