This is formula sheet for physics

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10. Physics Units

11. Vectors

12. Vectors
Notation:
Magnitude:
Dot product :
Cross product :

13. Kinematics

14. Kinematics
Average and Instantaneous Vel. and Accel.
Motion in a straight line with constant a :
Relative Velocity :

15. Projectile Motion :
Kinematics

16. NLM

17. NLM
Linear Momentum :
Newton’s first law : inertial frame.
Newton’s second law :
Newton’s third law :
Frictional Force : fstatic, max
= 𝜇s
N, f kinetic
=𝜇k
N
Banking angle :

18. Centripetal force :
Pseudo force :
Minimum speed to complete vertical circle :
Conical pendulum :
NLM

19. WPE

20. Work:
Kinetic energy :
Potential energy : for conservative F
Work done by conservative force is path
independent and depends only on initial
and final points :
WPE

21. Work - energy theorem : W = ∆ K
Mechanical energy : E = U + K
Conserved if forces are conservative in nature.
Power :
WPE

22. COM

23. Centre of mass :
CM of few useful configurations:
1. m1
, m2
separated by r:
2. Triangle (CM ≡ Centroid)
COM

24. 3. Semicircular ring:
4. Semicircular disc :
5. Hemispherical shell:
6. Solid Hemispheres:
COM

25. 7. Cone : the height of CM from the base is h/4 for
the solid cone and h/3 for the hollow cone.
Motion of the CM: M = ∑mi
COM

26. Collisions

27. Collision:
Momentum conservation : m1
v1
+ m2
v2
= m1
v1
’+m2
v2
’
Elastic Collision:
Coefficient of restitution:
Collisions
If v2
= 0 and m1
<< m2
then v1
’ = -v1
.
If v2
= 0 and m1
>> m2
then v2
’ = 2v1
.
Elastic collision with m1
= m2
: v1
’ = v2
and v2
’ = v1
.

28. Perfect Elastic Collision
Collisions

29. Rotational Dynamics

30. Rotational Dynamics
Angular velocity:
Angular Accel.:
Rotation about an axis with constant 𝛼:
Moment of Inertia:

31. Radius of Gyration:
Angular Momentum :
Torque:
Rotational Dynamics

32. Conservation of
Equilibrium condition:
Kinetic Energy:
Dynamics:
Rotational Dynamics

33. Gravitation

34. Gravitation
Gravitational force:
Potential energy:
Gravitational acceleration:

35. Variation of g with depth:
Variation of g with height:
Effect of non-spherical earth shape on g:
g at pole > g at equator (∵ Re
- Rp
≈ 21 km)
Effect of earth rotation on apparent weight:
Mg𝜃
’ = mg - m𝜔2
Rcos2
𝜃
Gravitation

36. Orbital velocity of satellite :
Escape velocity :
Kepler’s laws :
First: Elliptical orbit with sun at one of the focus.
Second : areal velocity is constant .
Third : T2
𝛼 a3
. In circular orbit
Gravitation

37. SHM

38. SHM
Hooke’s law : F = - kx (for small elongation x.)
Acceleration :
Time period :
Displacement : x = A sin (𝜔t + 𝜙)
Velocity :

39. Potential energy :
Kinetic energy :
Total energy :
SHM

40. Simple pendulum:
Physical Pendulum :
SHM

41. Springs in series :
Springs in parallel : keq
= k1
+ k2
SHM

42. Superposition of two SHM’s :
x1
= A1
sin 𝜔t, x2
= A2
sin(𝜔t + 𝛿)
x = x1
+ x2
= A sin (𝜔t + ∊)
SHM

43. Wave Motion

44. Notation : Amplitude A, Frequency v, Wavelength 𝜆,
period T, Angular Frequency 𝜔, Wave number k,
Progressive wave travelling with speed v:
Y = f(t - x/v), ⇝ + x, y = f(t + x/v), ⇝ - x
Progressive sine wave:
y = A sin(kx -𝜔t) = A sin(2𝜋(x/𝜆 - t/T))
Wave Motion

45. Interference :
y1
= A1
sin(kx - 𝜔t), y2
= A2
sin(kx - 𝜔t + 𝛿)
y = y1
+ y2
= Asin(kx - 𝜔t + ∊)
Waves On String

46. Standing Waves:
y1
= A1
sin(kx - 𝜔t), y2
= A2
sin(kx - 𝜔t)
y = y1
+ y2
= (2A cos kx)sin𝜔t
Waves On String

47. String fixed at both ends:
1. Boundary conditions y = 0 at x = 0 and at x = L
2. Allowed freq:
3. Fundamental/1st
harmonics :
4. 1st
overtone/2nd
harmonics:
5. 2nd
overtone/3rd
harmonics :
6. All harmonics are present.
Waves On String

48. String fixed at one end:
1. Boundary conditions: y = a at x = L
2. Allowed freq:
3. Fundamental/1st
harmonics :
4. 1st
overtone/3rd
harmonics :
5. 2nd
overtone/5th
harmonics:
6. Only odd harmonics are present.
Waves On String

49. Sound Waves

50. Displacement wave : s = s0
sin 𝜔 (t - x/v)
Pressure wave : p = p0
cos 𝜔(t-x/v), p0
= (B𝜔/v) s0
Speed of sound waves :
Sound Waves

51. Closed organ pipe:
1. Boundary condition: x = 0 at y = 0
2. Allowed freq:
3. Fundamental/1st
harmonics :
4. 1st
overtone/3rd
harmonics:
5. 2nd
overtone/5th
harmonics:
6. Only odd harmonics are present.
Sound Waves

52. Open organ pipe:
1. Boundary condition ; x = 0 at y = 0
Allowed freq:
2. Fundamental/1st
harmonics:
3.1st
overtone/2nd
harmonics:
4. 2nd
overtone/3rd
harmonics:
5. All harmonics are present.
Sound Waves

53. Beats: two waves of almost equal frequencies 𝜔1
≈ 𝜔2
P1
= P0
sin 𝜔1
(t - x/v), P2
= sin 𝜔2
(t - x/v)
P = P1
+ P2
= 2P0
cos ∆𝜔(t - x/v) sin 𝜔(t - x/v)
𝜔= (𝜔1
+ 𝜔2
)/2, ∆𝜔 = 𝜔1
- 𝜔2
(beats freq.)
Doppler Effect:
Where, v is the speed of sound in the medium, u0
is the
speed of the observer w.r.t. the medium, considered positive
when it moves towards the source and negative when it
moves away from the source, and us
is the speed of the
source w.r.t. the medium, considered positive when it moves
towards the observer and negative when it moves away
from the observer.
Sound Waves

54. Fluid Mechanics

55. Fluid Mechanics
Hydrostatic pressure : P = pgh
Buoyant force : FB
= pVg = Weight of displaced
liquid
Equation of continuity : A1
V1
= A2
V2
Bernoulli’s equation:
Torricelli’s theorem :

56. Fluid Mechanics
Viscous force:
Stoke's law : F = 6 𝜋𝜂r𝜐
Poiseuille's equation:
Terminal velocity:

57. Fluid Mechanics
Surface tension: S = F/l
Surface energy: U = SA
Excess pressure in bubble :
∆pair
= 2S/R, ∆psoap
= 4S/R
Capillary rise:

58. Temperature And Thermal
Expansion

59. Temperature And Thermal
Expansion
Temp. scales:
Ideal gas equation: pV = nRT, n : number of moles
Thermal expansion:
L = L0
(1 + 𝛼∆T), A = A0
(1 + 𝛽∆T) , = V0
(1 + 𝛾∆T)
𝛼 = 𝛽/2 = 𝛾/3
Thermal stress of a material :

60. Heat Transfer

61. Heat Transfer
Conduction:
Thermal resistance:

62. Kirchhoff’s law:
Wien’s displacement law: 𝜆m
T = b
( b = 3 × 10-3
m-k)
Stefan-Boltzmann law: (σ=5.6704×10−8
W/m2
·K)
Newton’s law of cooling :
Heat Transfer

63. KTG

64. KTG
General : M = mNA
, k = R/NA
RMS Speed :
Average speed :
Most probable speed :
Pressure :
Equipartition of energy: K = kT for each
degree of freedom. Thus, K = kT for molecule
having f degrees of freedom.
Internal energy of n moles of an ideal gas is
U = nRT.

65. Specific heat :
Latent heat : L = Q/m
Specific heat at constant volume:
Specific heat at constant pressure:
Relation between Cp
and Cv
: Cp
- Cv
= R
Ratio of specific heats : 𝛾 = Cp
/Cv
KTG

66. Relation between U and Cv
: ∆U = nCv
∆T
Specific heat of gas mixture:
Molar internal energy of an ideal gas U = RT,
f = 3 for monatomic and f = 5 for diatomic gas.
KTG

67. Thermodynamics

68. Thermodynamics
First law of thermodynamics : ∆Q = ∆U + ∆W
Work done by the gas:
Adiabatic process : ∆Q = 0, PV𝛾
= constant

69. Efficiency of the heat engine:
Coeff. Of performance of refrigerator :
Thermodynamics

70. Electrostatics

71. Electrostatics
Coulomb’s law :
Electric field :
Electrostatic energy :
Electrostatic potential :

72. Electric flux :
Gauss’s law :
Field of a uniformly charged ring on its axis :
Electrostatics

73. E and V of a uniformly charged sphere:
E and V of a uniformly charged spherical shell:
Electrostatics

74. Electrostatics
Field of a line charge:
Field of an infinite sheet:
Field in the vicinity of conducting surface:

75. Electric dipole moment :
Potential of a dipole :
Field of a dipole :
Torque on a dipole placed in
Pot. energy of a dipole placed in
Electrostatics

76. Capacitance

77. Capacitance
Capacitance : C = q/V
Parallel plate capacitor : C= ∊0
A/d
Spherical capacitor :

78. Cylindrical capacitor :
Capacitors in parallel : Ceq
= C1
+
C2
Capacitors in series :
Capacitance

79. Force between plates of a parallel plate
capacitor :
Energy stored in capacitor :
Energy density in electric field:
Capacitor with dielectric : C=KC0
Capacitance
C0
= ∊0
A/d

80. Current Electricity

81. Current Electricity
Current density : j = i/A = 𝜎E
Drift speed :
Resistance of a wire : R = pl/A, where p = 1/𝜎
Temp. dependence of resistance : R = R0
(1 + 𝛼∆T)
Ohm’s law : V = iR

82. Kirchhoff’s Laws :
(i) The junction law: The algebraic sum of all the
currents directed towards a node is zero i.e., ∑node
Ii
= 0.
(ii) The Loop Law: The algebraic sum of all the
potential differences along a closed loop in a circuit is
zero i.e. ∑loop
∆ Vi
= 0.
Resistors in parallel :
Resistors in series : Req
R1
+ R2
Current Electricity

83. Wheatstone bridge :
Balanced if R1
/R2
= R3
/R4
.
Electric Power : P = V2
/R = I2
R = IV
Current Electricity

84. Galvanometer as an ammeter :
ig
G = (i - ig
)S
Galvanometer as a Voltmeter :
VAB
= ig
(R + G)
Current Electricity

85. Charging of capacitors :
Discharging of capacitors :
Time constant in RC circuit : 𝜏 = RC
Current Electricity

86. Magnetism

87. Magnetic Field Due To
Current
Biot - Savart law :
Field due to a straight conductor :
Field due to an infinite straight wire :

88. Force between parallel wires :
Field on the axis of a ring :
Field at the centre of an arc :
Magnetic Field Due To
Current

89. Field at the centre of a ring :
Ampere’s law :
Field inside a solenoid :
Field inside a toroid :
Magnetic Field Due To
Current

90. Lorentz force on a moving charge :
Charged particle in uniform magnetic field :
Force on a current carrying wire :
Force on a charge in B

91. Magnetic moment of a current loop (dipole) :
Torque on a magnetic dipole placed in B:
Energy of a magnetic dipole placed in B:
Magnetism

92. Field of a bar magnet :
Angle of dip : Bh
= B cos 𝛿
Magnetism

93. EMI

94. EMI
Magnetic flux :
Faraday’s law :
Lenz’s Law : Induced current create a B-field
that opposes the change in magnetic flux.
Motional emf : e = Blv

95. Self inductance :
Self inductance of a solenoid : L = 𝜇0
n2
(𝜋r2
l)
Energy stored in an inductor :
Energy density of B field :
Mutual inductance :
EMI

96. Growth of current in LR circuit :
Decay of current in LR circuit :
Time constant of LR circuit : 𝜏 = L/R
EMI

97. AC

98. EMF induced in a rotating coil : e = NAB 𝜔 sin 𝜔t
Alternating current :
i = i0
sin(𝜔t + 𝜙), T = 2𝜋/𝜔
Average current in AC :
RMS current :
Energy : E = irms
2
RT
AC

99. Capacitive reactance :
Inductive reactance : XL
= 𝜔L
Impedance = Z = e0
/i0
AC

100. RC circuit :
LR circuit :
AC

101. LCR Circuit:
𝜐resonance
Power factor : P = erms
irms
cos𝜙
Transformer :
AC

102. Ray Optics

103. Laws of reflection :
(i) Incident ray, reflected ray,
and normal lie in the same plane
(ii) ∠i = ∠r
Plane mirror :
(i) the image and the object are
equidistant from mirror
(ii) virtual image of real object
Ray optics

104. Spherical mirror :
1. Focal length: f = R/2
2. Mirror equation :
3. Magnification :
Ray optics

105. Refractive index :
Snell’s Law :
Apparent depth :
Critical angle :
Ray Optics

106. Deviation by a prism :
𝛿 = i + i’ - A, general result
i = i’ for minimum deviation
𝛿m
= (𝜇 - 1)A, for small A
Ray Optics

107. Refraction at spherical surface :
Lens maker’s formula :
Ray Optics

108. Ray Optics
Lens formula :
Power of the lens : P in diopter if f in metre.
Two thin lenses separated by distance d :

109. Simple microscope : m = D/f in normal adjustment.
Compound microscope :
1. Magnification in normal adjustment :
2. Resolving power :
Ray Optics- Optical
Instruments

110. Astronomical telescope :
1. In normal adjustment :
2. Resolving power :
Ray Optics- Optical
Instruments

111. Dispersion by prism with small A and i :
1. Mean deviation : 𝛿y
= (𝜇y
- 1) A
2. Angular dispersion: 𝛳 = (𝜇v
- 𝜇r
)A
Dispersive power : (if A and i small)
Dispersion without deviation :
(𝜇y
- 1) A +(𝜇y
’ - 1)A’ = 0
Deviation without dispersion :
(𝜇v
- 𝜇r
)A = (𝜇v
’ - 𝜇r
’)A’
Ray Optics- Dispersion

112. Wave Optics

113. Path difference :
Phase difference :
Interference Conditions :
Wave Optics-YDSE

114. Intensity :
Fringe width :
Optical path : ∆x’ = 𝜇∆x
Wave Optics-YDSE

115. Diffraction from a single slit :
For minima ; n𝜆 = b sin 𝛳 ≈ b(y/D)
Malus law : I = I0
cos2
𝛳
Wave Optics-Diffraction

116. Atoms

117. Energy in nth Bohr orbit :
Radius of the nth Bohr orbit :
Quantization of the angular momentum :
Atoms

118. Atoms
Wavelength of emitted radiation : for a transition
from nth to mth state :
Photon energy in state transition : E2
- E1
= hv

119. Photoelectric Effect

120. Photoelectric Effect
Photon’s energy : E = h𝜐 = hc/𝜆
Photon’s momentum : P = h/𝜆 = E/c
Max. KE of ejected photoelectron : Kmax
= h𝜐 - 𝜙
Threshold freq. in photoelectric effect : 𝜐0
= 𝜙/h
Stopping potential :
De broglie wavelength: 𝜆 = h/p

121. Radioactivity

122. Radioactivity
Nuclear radius : R = R0
A1/3
, R0
≈ 1.1 × 10-15
m
Decay rate :
Population at time t : N = N0
e-𝜆t
Half life : t1/2
= 0.693/𝜆
Average life : tav
= 1/𝜆
Population after n half lives : N = N0
/2n

123. Nuclei

124. Nuclei
Mass defect : ∆m = [Zmp
+ (A - Z)mn
] - M
Binding energy : B = [Zmp
+ (A -Z)mn
- M]c2
Energy released in nuclear reaction : ∆E = ∆mc2
Where ∆m = mreactants
- mproducts
.

125. Semiconductors

126. Half Wave Rectifier :
Full Wave Rectifier :
Semiconductors

127. Current in a transistor : Ie
= Ib
+ Ic
𝛼 and 𝛽 parameters of a transistor :
Semiconductors

128. Semiconductors
Logic Gates :
A B AND
AB
OR
A+B
NAND
AB
NOR
A+B
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0

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131. Started on
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Ends at
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132. Unlimited DOUBT solving on doubt
App 8 AM- 11 PM
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Papers
20 All India Level tests

134. ₹10,000
How to Avail Discount ?
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Visit: https://vdnt.in/JEECCE
Special Discount for this class
Link in Description
₹4,000/-
(incl. of all taxes)

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