*Measurements*

- 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 - θ = s/r
- 2π rad = 3600
- 3600 = 1 revolution
- 1 radian = 57.30
- 1 degree = 60 minute
- 1 minute = 60 seconds
- Angle at circle is 2π radian.
- Angle at sphere is 4π steradian.
- Volume of slid cylinder = πr2l
- Area of sphere = 4πr2
- Volume of sphere = 4/3 πr3
- Dimension of velocity = [LT-1]
- Dimension of acceleration= [LT-2]
- Energy of photon; E = hf
- Time period of pendulum; T = 2π

*Vectors_and_equilibrium*

- Commutative property of vector= A+B = B+A
- Fx =F cosθ
- Fy = Fsinθ
- F =
- A.B = AB cos θ
- A x B = AB sin θ
- Scalar product; work and power
- Vector product; torque
- τ = r x F
- First condition of equilibrium; ∑F = 0
- Second condition of equilibrium; ∑τ = 0

*Motion_and_Force*

- v = s/t
- a = v/t
- vf = vi +at
- s = vit + ½ at2
- 2as = vf2 – vi2
- S = vave x t
- Vave =( vi + vf )/2
- g = 9.8 ms-2 = 32 ft-2
- F = ma
- a = v/t
- P = mv
- P = F t
- Impulse; J = F x t = ∆P
- J = ∆P
- Law of conservation of momentum; ∆p = 0
- 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*

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

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