# Measurements

1. 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. Angle at circle is 2π radian.
9. Angle at 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

1. Commutative property of vector= A+B = B+A
2. Fx =F cosθ
3. Fy = Fsinθ
4. F =
5. A.B = AB cos θ
6. A x B = AB sin θ
7. Scalar product; work and power
8. Vector product; torque
9. τ = r x F
10. First condition of equilibrium; ∑F = 0
11. Second condition of equilibrium; ∑τ = 0

# Motion_and_Force

1. v = s/t
2. a = v/t
3. vf = vi +at
4. s = vit + ½ at2
5. 2as = vf2 – vi2
6. S = vave x t
7. Vave =( vi + vf )/2
8. g = 9.8 ms-2 = 32 ft-2
9. F = ma
10. a = v/t
11. P = mv
12. P = F t
13. Impulse; J = F x t = ∆P
14. J = ∆P
15. Law of conservation of momentum; ∆p = 0
16. Elastic collision in one dimension; [v1 + v2] = [v1’+ v2’]

Motion in two dimension
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
Chap No.11 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

Chap No. 12 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

Chap No. 13 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

Chap No. 14 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 )

Chap 18 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

Chap 19 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

Chap 20 NUCLEAR PHYSICS

1. Nuclear size is of the order of 10-14 m.
2. The mass of the nucleus is of the order of 10-27 kg.
3. ½ mv2 = Vq
4. Bqv = mv2/r
5. Bqv = mv2/r → m = Bqr/v
6. ½ mv2 = Vq → v2 = 2Vq/m
7. So m = qr2B2/2V
8. Δm = Zmp + Nmn – M(A,Z)
9. The binding energy in MeV is 931 x Δm.
10. The binding energy per nucleon = Eb/A.
11. 0n1 → 1H1 + -1β0 + antineutrino 12 MIN
12. ΔN/Δt =-λN
13. R =- ΔN/Δt =λN
14. N= N0e-λt
15. 1 Bq = 1 decay per second
16. 1 Ci = 3.70 x 1010 decay/s
17. λT ½ = 0.693
18. The charge on u,t and c, in term of electron is +2/3e.
19. The charge on s,t and b in term of electron is -1/3e.
20. proton =2U→D.
21. neutron=A-Z

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