## Chapter - 1 : Measurement and Experimentation

i) Physical Quantity = Numerical value × Unit

ii) Vernier Caliper

a) Least count = value\ of\ one\ main\ scale\ division\ (n)\over Total\ number\ of\ division\ on\ vernier\ (n)

b) Vernier Reading =p × Least Count

*(p=p ^{th} division of the vernier scale that coincides with the main scale)*

c) Total Reading =Main scale reading +Vernier Reading

**iii) Zero error in Vernier Caliper**

a) Positive zero error – taken as +ve

b) Negative zero error -taken as -ve

c) Correct Reading =Observed reading -Zero error (with sign)

**iv) Screw Gauge**

a) Least count = Pitch\ of\ the\ screw\over Total\ number\ of\ division\ on\ circular\ scale

b) Positive zero error – taken as +ve

c) Negative zero error -taken as -ve

d) Correct Reading =Observed reading -Zero error (with sign)

**v) Relation between time period and frequency of wave**

a) Time Period (T) = 1\over Frequency\ (f)

b) Frequency (f) = 1\over Time\ Period\ (T)

c) Time Period of pendulum (T) = 2π\sqrt{l\over g}

## Chapter - 2 : Motion in One Dimenion

i) Speed (V) = Distance\ (S)\over Time\ (t)

ii) Average Speed = Total\ Distance\ Travelled\over Total\ Time\ Taken

iii) Velocity (v) = Displacement \over Time

iv) Average Velocity (v) = Displacement \over Time\ time\ taken

v) Acceleration = Final\ velocity\ (v) – Intial\ velocity\ (u) \over Time\ internal\ (t)

vi) **Equation of motion **

a) v = u + at

b) S = ut + ½ at²

c) v² = u² + 2aS

- v = Final velocity,
- u = Initial velocity,
- a = acceleration and
- distance travelled (S)

## Chapter - 3 : Laws of Motion

i) Linear Momentum (p) = m × v

- m = mass
- v = velocity

ii) Change of momentum (△p) = m × (v-u)

iii) Force (F) = m × a

- m = mass
- a = acceleration

iv) Gravitational Force (F) = G m_{1}m_{2}/r²

v) Acceleration due to gravity (g) =GM/R²

**vi) Free Fall**

Downward Motion | Upward Motion |

(a) v = u + gt (b) h = ut + ½gt (c) v² = u² + 2gh | (a) v = u – gt (b) h = ut – ½gt (c) v² = u² – 2gh |

vii) Weight (W) = mass (m) × gravity (g)

## Chapter - 4 : Pressure in Fluid and Atomospheric Pressure

i) Pressure = Thrust\over Area

ii) Pressure in fluid = h×ρ×g

- h = depth
- ρ = density of liquid
- g = acceleration due to gravity

iii) Total pressure in a liquid = P_{o} + hρg

- P
_{o }= Atmospheric pressure

iv) F_1\over A_1=F_2\over A_2

## Chapter - 5 : Upthrust in Fluids

i) Upthrust (F_{B}) = Vρg

- V = volume of liquid displaced
- ρ = density of liquid
- g = acceleration due to gravity

ii) Density = Mass\over Volume

iii) Relative Density = Density\ of\ substance\over Density\ of\ water\ at\ 4ºC

iv)** Relation between density and RD**

- Density = RD × 1000 (in SI)
- Density = RD (in CGS)

v) RD = W_1\over W_1 – W_2

- W1 = Weight of body in air
- W
_{2}= Weight of body in water

vi) RD of a solid denser than water and insoluble in it

RD = W_1\over W_1 – W_2

- W
_{1}= Weight of body in air - W
_{2}= Weight of body in water

vii) RD of a solid denser than water and soluble in it

RD = Weight\ of\ solid\ in\ air\over Loss\ in\ weight\ of\ solid\ in\ liquid×RD of liquid

viii) RD of liquid = W_1 – W_2\over W_1 – W_3

- W
_{1}= Weight of body in air - W
_{2}= Weight of body in liquid - W
_{3}= Weight of body in Water

## Chapter - 6 : Heat and Energy

i) t K = 273 + t ^{o}C

ii) C\over 5=F – 32\over 9

## Chapter - 7 : Reflection of light

The number of images formed depends on the angle θº between the two mirrors. Following two cases are possible:

**Case – 1**: n = 360º/θº is odd,

- the number of images is n, when the object is placed symmetrically.
- the number of image is n-1, when the object is placed symmetrically.

**Case – 2**: n = 360º/θº is even, the number of images is always n – 1 for all positions of object.

**Position, size and Nature of images for concave mirror**

Position of object | At infinity |

Position of image | At the focus |

Size of image | Point size |

Nature of image | Real and Inverted |

Position of object | Beyond C |

Position of image | Between C and F |

Size of image | Diminished |

Nature of image | Real and Inverted |

Position of object | At C |

Position of image | At C |

Size of image | Same Size |

Nature of image | Real and inverted |

Position of object | Between C and F |

Position of image | Beyond C |

Size of image | Magnified |

Nature of image | Real and Inverted |

Position of object | At F |

Position of image | At infinity |

Size of image | highly Magnified |

Nature of image | Real and Inverted |

Position of object | Between Pole and F |

Position of image | Behind the mirror |

Size of image | Magnified |

Nature of image | Virtual and upright |

**Position, size and Nature of images for convex mirror**

Position of object | At infinity |

Position of image | At focus |

Size of image | Point sized |

Nature of image | Virtual and upright |

Position of object | At any other point |

Position of image | Between focus and pole |

Size of image | Diminished |

Nature of image | Virtual and upright |

**Mirror Formula**

i) f = 1\over2R

iii) **Lens Formula:** {1\over v} + {1\over u} = {1\over f}

- u = object distance from the mirror
- v = image distance from the mirror
- f = focal length

iv) **Linear Magnification (m) :**

- m = size\ of\ image\over size\ of\ object
- m = – Distance\ of\ image\over Distance\ of\ object

## Chapter - 8 : Sound

(i) Frequency (f) = 1\over Time\ Period\ (T)

**(ii) Relationship between the wavelength, velocity and frequency**

(a) VT = λ

(b) V = fλ

- λ = wavelength
- T = velocity
- V = Wave velocity

(iii) **Other formulae**

(a) V = \sqrt{E\over ρ}

(b) V = \sqrt{P\over ρ}

(c) V = \sqrt{γP\over ρ}

- E = Elasticity of medium
- ρ = density of the medium
- γ = 1.4

(d) V_{t} = V_{o} + 0.61 t

- V
_{o }= Velocity at 0ºC - V
_{t}= Velocity at tºC

## Chapter - 9 : Current electricity

(i)** Quantization of charge:** Q = ne

- Q = Charge
- n = no. of charge
- e = value of charge = 1.6 × 10
^{-19}C

(ii) Current (I) = Charge (Q)\over time (t)

(iii) Potential (V) = work\ (W) \over Charge\ (Q)

(iv) Potential Difference (V_{1} – V_{2}) = work\ (W) \over Charge\ (Q)

(v) **Ohm’s law:** V = IR

- V = Potential Difference
- I = Current
- R = Resistance