Friday, 24 July 2020

Physics Formulas related to all topics for Entry Test preparations - MDCAT, ECAT etc.

Physics Formulas related to all topics for Entry Test preparations - MDCAT, ECAT etc.
Here we have shared the Physics Formulas related to all topics for Entry Test preparations - MDCAT, ECAT, etc. It is very helpful to prepare for the entrance exams and reduces your time exponentially.

It includes formulas related to:


  • General Formulas
  • Entric Charges and fields formulas
  • Capacitance formulas
  • Current formulas
  • Resistance formulas
  • Magnetism formulas
  • Inductive and RCL Circuits formulas
  • AC circuits formulas
  • Electromagnetics formulas
  • Light




Measurements

1.      The smallest unit of measurement by;
Measurement tape → 1 cm or 1mm
Meter rule or half meter rule → 0.1 cm or 1 mm
Vernier caliper → 0.01 cm or 0.1 mm
Screw gauge → 0.001 cm or 0.01 mm
2.      θ = s/r
3.      2π rad = 3600
4.      3600 = 1 revolution
5.      1 radian = 57.30
6.      1 degree = 60 minute
7.      1 minute = 60 seconds
8.      The angle at the circle is 2π radian.
9.      The angle at the sphere is 4π steradian.
10.  Volume of slid cylinder = πr2l
11.  Area of sphere = 4πr2
12.  Volume of sphere = 4/3 πr3
13.  Dimension of velocity = [LT-1]
14.  Dimension of acceleration= [LT-2]
15.  Energy of photon; E = hf
16.  Time period of pendulum; T = 2π 

Vectors and equilibrium

17.  Commutative property of vector= A+B = B+A
18.  Fx =F cosθ
19.  Fy = Fsinθ
20.  F = 
21.  A.B = AB cos θ
22.  A x B = AB sin θ
23.  Scalar product; work and power
24.  Vector product; torque
25.  τ = r x F
26.  First condition of equilibrium; ∑F = 0
27.  Second condition of equilibrium; ∑τ = 0

Motion and Force

28.  v = s/t
29.  a = v/t
30.  vf = vi +at
31.  s = vit + ½ at2
32.  2as = vf2 – vi2
33.  S = vave x t
34.  Vave ( vi + vf )/2
35.  g = 9.8 ms-2 = 32 ft-2
36.  F = ma
37.  a = v/t
38.  P = mv
39.  P = F t
40.  Impulse; J = F x t = ∆P
41.  J = ∆P
42.  Law of conservation of momentum; ∆p = 0
43.  Elastic collision in one dimension; [v1 + v2] = [v1’+ v2’] 
44.  Magnitude of projectile velocity; Vf = 
45.  Height of projectile; H = vi2sin2θ/2g
46.  Time of flight; T = 2 vi sinθ/g
47.  Time of summit or time to reach to highest point; T = vi sinθ/g
48.  Range; R = vi2 sin 2θ/g
49.  Rmax = vi2/g
50.  R = Rmax at 450

Work and Energy

51.  W = Fd cosθ
52.  Power; p=W/t or p =Fv
53.  1 watt = Js-1
54.  1 hp = 746 watts
55.  K.E = ½ mv2
56.  P.E = mgh
57.  Efficiency = output/input = W x D/P x d
58.  Absolute potential energy =Fr = - GmMe/Re (- because work is done against gravity)
59.  Gravitational potential = E/m = GMe/Re
60.  For escape velocity compare K.E with Absolute potential energy; vesc =  → vesc = 
61.  G = 6.67 x 10-11 Nm2kg-2
62.  Re = 6.4 x 106 m
63.  Me = 6 x 1024 kg
64.  Vesc = 11.2 x 103 ms-1
65.  Wh = K.E + fh → (Wh = loss in potential energy)
66.  Loss in P.E = Gain inn K.E + work done against friction
67.  E = mc2 →(c= 3 x 108 ms-1)

Rotational and circular motion

68.  Angular velocity; ω = ∆θ/∆t
69.  Angular acceleration; α = ∆ω/∆t → a = α x r
70.  v = r ω
71.  Fc = mv2/r
72.  ac = -(v2/r)
73.  Centrifugal force= mv2/r
74.  F sin θ = mv2/r
75.  F cos θ = mg
76.  Tan θ = v2/gr
77.  Τorque = r F = rma = rm (rα) 🙁 r2m)α = I α
78.  Moment of inertia; I = mr2
79.  Ring or thin walled cylinder inertia(I) = MR2
80.  Disc or solid cylinder inertia = ½ MR2
81.  Disc inertia = ½ M (R22 + R12 )
82.  Solid sphere inertia = 2/5 MR2
83.  Solid rod or meter stick inertia = 1/12 Ml2
84.  Rectangular plate inertia = 1/12 M (a2+b2)
85.  Angular momentum = L = r x p = r mv = rmrω =r2mω = Iω
86.  L = rmv → L/t = rmv/t = rma = rF = τ
87.  L/t = τ
88.  Linear kinetic energy = ½ mv2
89.  Rotational kinetic energy = ½ Iω2
90.  Velocity of hoop = v = 
91.  Velocity of disc = v = 
92.  Critical velocity = v = 7.9 km2
93.  The orbital velocity = v = 
94.  Lift at rest → T =w
95.  Lift moving downward → T = w – ma
96.  Lift moving upward → T = w + ma
97.  Lift falling freely = T  mg-ma = 0
98.  Frequency for artificial satellite → f = 

Fluid dynamics

99.  Drag force → Fd = 6 πη r v
100.       Terminal velocity → vt = 
101.       Continuity equation → A1 v1 = A2 v2
102.       Av=∆V/∆t = constant
103.       ∆m/∆t = ρ ∆V/∆t
104.       Bernoulli’s Equation = P + ½ ρv2 + ρgh = constant
105.       Torricelli’s Theorem → v = 
106.       Flow meter or the venture meter → v1 = 

Oscillation

107.       Frequency → f=1/T
108.       Angular frequency → ω = 2πf
109.       Time period → T = 2π/ω
110.       Velocity of projection → vy = ω
111.       Simple pendulum time period → T = 2π 
112.       Simple pendulum potential energy = ½ kx2
113.       Simple pendulum kinetic energy = ½ kx02 -½ kx2
114.       Total energy of simple pendulum = ½ kx02
115.       Resonance frequency = Fn = nf1
116.       Phase → θ =ω t

Waves

117.       Transverse wave speed →  
118.       Longitudinal waves speed → 
119.       Phase change→ 2π = λ
120.       Phase difference → δ = 2π/λ
121.       Speed of sound by newton → v =  = 281 ms-1
122.       Laplace correction → v =  = 332 ms-1

ELECTROSTATICS

123.       1 e = 1.602 x 10-19 C
124.       Q = ne
125.       Coulomb’s Law; F = k  
126.       K =  
127.       K = 9.0 x 109 N m2 C-2
128.       εo = 8.85 x 10 -12 C2 N-1 m-2
129.       εr = 
130.       Fmed =  
131.       E =  =  = K 
132.       Ф = E A cos θ = N m2 C-1
133.       Ф = 
134.       E due to sheet of charge;  E = 
135.       E due to charge palates;     E = 
136.       V =  =                             Volt = Joule / Coulomb
137.       Electric potential energy;  U = 
138.       Electric potential;     V =   =  =  
139.       Potential Gradient =  E = -  
140.       1 eV =1.602 x 10-19 C x 1V           →   (1 eV = 1.602 x 10-19 J)
141.       C =  = C V-1 = farad
142.       Charge density;   σ = 
143.       Cvac =  =  =  
144.       εr = Cmed / Vvac
146.       Capacitors In Series;
147.       Q = Q1 = Q2 =Q3
148.       V =V1 + V2 + V3
149.       1/Ce = 1/C1 + 1/C2 + 1/C3
150.       Capacitors In Parallel;
151.       Q = Q1 = Q2 = Q3
152.       V = V1 + V2 +V3,
153.       Ce = C1 + C2 + C3
154.       Electric dipole; P = q d
155.       Energy = U =   =   (Ed)2
156.       Energy density; E2
157.       Maximum charge on capacitor = C x e.m.f
158.       q/q0 = 63.2 %          →for charging
159.       q/q0 = 36.7 %          →for discharging
160.       q = q0 (1-e-t/RC )       →for charging
161.       q = q0 e-t/RC               →for discharging

CURRENT ELECTRICITY

162.       Current, I = Q/t → C s-1 = A
163.       Drift velocity order = 10-5 m/s.
164.       V = IR
165.       Tan θ = I/V = 1/R
166.       Resistance, R = V/I  → 1Ω = 1V/1A
167.       R = ρ L/A  → Ω.m
168.       Conductance, G = 1/R  → Siemen(S)  or mho
169.       Conductivity, σ = 1/ρ =L/RA   →mho/m or S/m
170.       Pure metals R inc with T inc.
171.       Electrolytes and insulators, R dec with T inc.
172.       ΔR = αR0 T   → RT  = R0 (1+αT)
173.       Temperature co-efficient of Resistance, α =  RT  – R0/R0T   → K-1
174.       Resistivity, ρ T  = ρ 0 (1+αT)  OR   α =  ρ T  – ρ 0/ ρ 0T   → K-1
175.       Electromotive Force, ε = W/q     → 1 volt = 1 joule/coulomb
176.       Open circuit, I = 0 so  V= ε
177.       Terminal Voltage, Vt = ε - Ir
178.       Power,  P = W/t = VI    → 1 Watt = 1V x 1A
179.       1 kWh = 1 unit of electrical energy
180.       1 J = 1W x 1s
181.       Maximum output power,  (Pout)max = ε2 /4r = ε2 /4R
182.       Thermo emf,    ε = αT + ½ βT2
183.       KCL, ƩI = 0
184.       KVL,  Ʃε = ƩV = ƩIR
185.       KCL based on L.O.C.O.CHARGE
186.       KVL based on L.O.C.O.ENERGY
187.       Wheatstone Bridge,  X = PQ/R
188.       Potentiometer,  ε2 /ε1 = I2 /I1
189.       Tan θ = I/V = 1/R

ELECTROMAGNETISM

190.       Force on current carrying wire, F=BIL sin θ.
191.       Magnetic field or magnetic induction, B = F/IL →1 tesla =1 NA-1 m-1 = 1 Wb m-2
192.       1 T = 104 G
193.       Magnetic Flux,    Ф = B A cos θ     → 1 Wb = 1 N m A-1.
194.       Ampere’s Law,   B  I/r = μ0 (I/2πr)    OR      ƩB.ΔL = μ0 I
195.       Bnet = B1 + B2
196.       Magnetic field due to current carrying solenoid,  B = μ0 n I  → n=N/L
197.       Motion of charge particle in uniform magnetic field,    F=q v B sin θ
198.       Centripetal Force = Magnetic force   → mv2/r = qvB
199.       Time period of charge particle in B,        T = 2πm/qB
200.       Frequency of charge particle in B,       f = qB/2πm
201.       Velocity selector,              FE = FM  →   qE = qvB     → v = E/B
202.       Torque on current carrying coil,    τ = NBIA cos θ
203.       Ρestoring torque,      τ = C θ
204.       Galvanometer,   NBIA cos θ = C θ    → I = Cθ/NAB    → I  θ
205.       Conversion of galvanometer into ammeter,  small R connected in parallel
206.       Conversion of galvanometer into voltmeter,     large R in series are connected
207.       Ammeter,   Rs = Rg Ig / (I – Ig)      → Ideal ammeter → 0 R
208.       Voltmeter,   Rh = (V/I­g) – Rg                → Ideal voltmeter → infinite R

ELECTROMAGNETIC INDUCTION

209.       Faraday’s Law,   ε  N (ΔФ/Δt)    → ε = N (ΔФ/Δt )
210.       Lenz Law,     ε = –N (ΔФ/Δt ) 
211.       Flux motional emf,   ε = Blv sin θ
212.       Rate of work done,   W= Bilv
213.       Rate of production of electrical energy,    energy =ε I
214.       W = energy   → Bilv = εI  → ε = Blv
215.       Power,   P = F v
216.       ε = L ΔI/Δt   or ε = N ΔФ/Δt   → LI = NФ
217.       Self-Inductance,    L = NФ /I
218.       ε = M ΔI/Δt   or ε = N ΔФ/Δt   → MI = NФ
219.       Mutually inductance,   M = NФ /I
220.       F = 1/T
221.       Induced emf,  ε = NAB cosωt   or  NAB ω sinωt
222.       ε = εmax sin ωt
223.       Back emf,   V = ε + IR
224.       Ns / Np = Vs / Vp = Ip /Is
Chap 16    PHYSICS OF SOLIDS
225.       Elastic modulus = 
226.       Tensile stress = 
227.       Tensile strain = 
228.       Young modulus =     = Nm-2
229.       Shear stress = 
230.       Shear strain =   = tan θ
231.       Shear modulus = rigidity modulus =  = 
232.       Bulk or volume stress = 
233.       Bulk modulus (in fluids) = Δp =  
234.       Volume strain =- 
235.       Bulk modulus =  = 
236.       Stress  strain (Hook’s law)
237.       A =  r2
238.       W = ½Fe   (work done on stretching wire).
239.       Strain energy = ½ F e
240.       Strain energy per unit volume =   = ½ (stress) (strain )

DAWN OF MODERN PHYSICS

241.       E = m0  c2
242.       L= L0  
243.       T = t0 
244.       M = m0 
245.       λmax T = 0.2898 x 10-2 m k     (Wein’s displacement law)
246.       E = σ T4                                     (Steffan-Bolts Law)
247.       σ = 5.67 x 10-8 Wm-1 K-4
248.       E = n h f
249.       K.Emax = e V0
250.       K.Emax = h f – Ф
251.       H f0 = Ф =  
252.       K.Emax = hf - Hf0
253.       Hf = K.E +hf’
254.       P= 
255.       Δλ = 1-
256.        =  +  1-
257.       Ephoton = Eelectron + Epositron
258.       Photon rest mass energy = 2m0c2 = 1.02 MeV
259.        = mve-  + mve+
260.       λ =  = 
261.       Δp =           and         Δx = λ
262.       (Δp)(Δx) = h
263.       (ΔE)(Δt) = h

ATOMIC SPECTRA

264.        = R (  -  )
265.       R =E0 / hc = 1.097 x 107m-1.
266.       mvr = nh/2π.
267.       h = planks constant = 6.6256 x 10-34 j s.
268.       E = hf = En – Ep
269.       rn =  
270.       En = -  
271.       En  = = 2.17 x 10-18 j/ n2 = +13.6 ev/ n2
272.       rn  = n2 r1 → r1 = 0.53 0A.
273.       1 0A = 10- m
274.       2πr=nλ
275.       eV → hfmax = hc/λmin
276.       λmin = hc/eV
277.       excited state for 10-8 s.
278.       metastable state for 10-3 s

NUCLEAR PHYSICS

279.       Nuclear size is of the order of 10-14 m.
280.       The mass of the nucleus is of the order of 10-27 kg.
281.       ½ mv2 = Vq
282.       Bqv = mv2/r
283.       Bqv = mv2/r → m = Bqr/v
284.       ½ mv2 = Vq → v2 = 2Vq/m
285.       So m = qr2B2/2V
286.   Δm = Zmp + Nmn – M(A,Z)
287.       The binding energy in MeV is 931 x Δm.
288.       The binding energy per nucleon = Eb/A.
289.       0n1 → 1H1 + -1β0 + antineutrino 12 MIN
290.       ΔN/Δt =-λN
291.       R =- ΔN/Δt =λN
292.       N= N0e-λt
293.       1 Bq = 1 decay per second
294.       1 Ci = 3.70 x 1010 decay/s
295.       λT ½ = 0.693
296.       The charge on u,t and c, in term of electron is +2/3e.
297.       The charge on s,t and b in term of electron is -1/3e.
298.       proton =2U→D.
299.        neutron

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