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=pth 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 m1m2/r²

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

vi) Free Fall

Downward MotionUpward Motion

(a) v = u + gt

(b) h = ut + ½gt²

(c) v² = u² + 2gh

(a) v = u – gt

(b) h = ut – ½gt²

(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 = Po + hρg

  • Po = Atmospheric pressure

iv) F_1\over A_1=F_2\over A_2

Chapter - 5 : Upthrust in Fluids

i) Upthrust (FB) = 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
  • W2 = 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

  • W1 = Weight of body in air
  • W2 = 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

  • W1 = Weight of body in air
  • W2 = Weight of body in liquid
  • W3 = Weight of body in Water

Chapter - 6 : Heat and Energy

i) t K = 273 + t oC

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,

  1. the number of images is n, when the object is placed symmetrically.
  2. 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 objectAt infinity
Position of imageAt the focus
Size of imagePoint size
Nature of imageReal and Inverted
Position of objectBeyond C
Position of imageBetween C and F
Size of imageDiminished
Nature of imageReal and Inverted
Position of objectAt C
Position of imageAt C
Size of imageSame Size
Nature of imageReal and inverted
Position of objectBetween C and F
Position of imageBeyond C
Size of imageMagnified
Nature of imageReal and Inverted
Position of objectAt F
Position of imageAt infinity
Size of imagehighly Magnified
Nature of imageReal and Inverted
Position of objectBetween Pole and F
Position of imageBehind the mirror
Size of imageMagnified
Nature of imageVirtual and upright

Position, size and Nature of images for convex mirror

Position of objectAt infinity
Position of imageAt focus
Size of imagePoint sized
Nature of imageVirtual and upright
Position of objectAt any other point
Position of imageBetween focus and pole
Size of imageDiminished
Nature of imageVirtual 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) :

  1. m = size\ of\ image\over size\ of\ object
  2. 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) Vt = Vo + 0.61 t

  • Vo = Velocity at 0ºC
  • Vt = 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 (V1 – V2) = work\ (W) \over Charge\ (Q)

(v) Ohm’s law: V = IR

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