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* DIMENSIONAL FORMULAE ——= © OF e-—— a PHYSICAL QUANTITIES | S.No | Physical quantity eee ait ities Dimensions | Dimensional formula 1. | Area Length x breadth [17] [M°L? T°] 2. | Volume Length x breadth x height | [L?] [M°L? T°] 3. | Mass density Mass/volume [M/L?] or [ML] [ML? T°] 4. | Frequency 1/time period (tT"] [M°L? T'] 5. | Velocity, speed Displacement /time [L/T] [M°LT7'] 6. | Acceleration Velocity /time [LT] /[7T] [M°LT~?] %. | Force Mass x acceleration [MLT~?] [MLT~] 8. | Impulse Force x time [MLT~][T] [MLT“*] 9. | Work, Energy Force x distance (MLT~?][L] (ML? T7] 10. | Power Work /time (MU? T*)/[1] [ML? T3] 11. | Momentum Mass x velocity [mM] [LT~"] [MLT~"} 12. | Pressure, stress Force/area [MLT?]/(U7] [ML*T?] 13. | Strain Change in dimension =| [1}/[t] or (L'Y/I']] [M°L° T°] Original dimension ie . A 7-2 17-2 14. | Modulus of elasticity | Stress/strain ae [ML'T~] 15. | Surface tension Force/length ([MLT~?]/[L] [ML° T-2] 16. | Surface energy Energy/area (ML? T-?]/[L?] [ML° T~7] 17%. | Velocity gradient | Velocity/distance [LT']/[L] [M°L° T*] 18. | Pressure gradient | Pressure/distance (ML'T~*]/[t] [ML* 177] 19. | Pressure energy Pressure x volume (ML*T~7] [L?] [ML? T"?] wm, | Set [Rees | OmETTS eT 2. | ae oe Arc/radius [LI/[L) [M°L? T°] 22. | [rigonometr oitic.)| Length/length (L)/(L] [M°L° T°] 23. | Angular velocity Angle/time (L°}/{T] [mMoL? T*] NOTE: 7 Dimensions help us to check the correctness of equations. m=) [M]-Mass [L]-Length [T]-Time / : amie hoes — eo Of oo— A ‘. Relationship with . - on a S.No | Physical quantity Lae phaseal arte Dimensions Dimensional formula 24. | Angular acceleration | Angular velocity/time (T)/[T] [M‘L' T-3] 25. | Radius of gyration Distance [L] [M°LT°] 26. | Moment of inertia Mass x (radius of gyration)” [M] [L”] [ML? T°] Moment of inerti: lar 2 A 27-1 27. | Angular momentum Leroi inertia x angul [ML*] [T"] [ML? T*] 28. | Moment of force, | Force x distance [MLT~?] [L] [ML? T?] moment of couple 29. Torque ate momentum/time, [ML? T']/ [T] [ML? T=] rr or Force x distance (MLT~?] [L] 30. | Angular frequency | 2m x Frequency (T*] [M°L°T"*] 31. | Wavelength Distance [L] [M°LT°] 32. | Hubble constant Recession speed/distance (LT“}/[L] [M°L°T™'] 33. | Intensity of wave (Energy/time)/area (ML? T?/T]/[L"] [ML°T-?] 34. | Radiation pressure Intensity of wave [MT~*]/[LT~*] [ML* T?] Speed of light 35. | Energy density Energy / volume [ML? T7]/[L*] [ML T*] 36. | Critical velocity Reynold’s number x coefficient of viscosity | [M°L° T°] [ML T~1] [M°LT*'] Mass density = radius [ML~*][L] 5 4 by leration due to 21/2 2. Oo, 7-1 37. | Escape velocity vets lesion oe Bu: (LT?) x [L] [M°LT™] 38. | Heat energy, internal | Work (= Force x distance) | [MLT~*] [L] [ML? T?] energy 39. | Kinetic energy (1/2) mass x (velocity) * [M] [LT]? [ML?T-?] 40. Potential Mass ~ acceleration M] [LT~27 [L ‘ML? T-2 er eee due to gravity x height Ca) Cer C J 41. | Rotational kinetic % x moment of inertia x | [ML?T°] [ML’]x[T“F; [ML? T] energy (angular velocity)” 42. | Efficiency Output work or energy [ML? T~7] [M°L°T°] Input work or energy [ML? T-*] | 43. | Angular impulse Torque x time [ML? T*] [T] [ML? T*] 44, | Gravitational Force x (distance)? [MLT~*] [L?] [M13 T-2] constant mass X mass [M] [M] 45. | Planck constant Energy/frequency (ML? T*] /[T“] _[ML? T*] NOTE : ‘3 Dimensions help us to check the correctness of equations. [M] - Mass [L] - Length [T] - Time N - * DIMENSIONAL FORMULAE —-°°OF-- w PHYSICAL QUANTITIES" S.No | Physical quantity the net ‘ties Dimensions | Dimensional formula Electric dipole IML? T'] 0 O. | goeae Torque/electric field Taree [M°LTA] Electric field strength Potential difference [ML? T3A~‘] “3 y-t es or electric intensity distance [L] hicall ad Magnetic field, Fi 67. | magnetic Fux density, | [Gamoeetengty | (MET VIANA] | [ML°T-2A~ magnetic induction 9 68. | Magnetic flux Magnetic field x area (MT~?A~*] [L?] (ML? T-?A~*] Magnetic flux (ML? T-2A71] 27-2 y-2 Inductai lr decane ed 69. inductance ret TAT [ML*T*A*] 70. | Magnetic dipole Torque /magnetic field [ML T*)/[MT 7A‘) monn . or or [M°L? TA] current x area [A] [L7] 71. | Magnetic field Magnetic moment [L2A] 4 strength, magnetic [M°L*TA] intensity or magnetic (Volume) [L*] moment density 72. | Permittivity constant Charge x charge [AT] [AT] [ML T4A2] (of free space) 4m x electric force x (distance! [MLT~*] [L}? 73. | Permeability constant | 2m x force x distance [M°L°T°) [MLT*) (1) [MLT-2A72] (of free space) (current x current x length) [A] [A][L] oat Speed of light in vacuum FS oe wt 0) 0-70 74. | Refractive index “Spend ct eG wali [LT yr] [M°L°T?] Farada Avogadro constant x 0,0 -1 7 consti donatary charge [AT ]/{mol] [M'L'TA mol] 76. | Wave number 2n/wavelength [M°L°T°]/[L] [M°L"*T°] ate ay flux, Radiant Energy emitted/time [ML? T-7]/[T] [ML? T-3] Luminosity of radiant | pas eae 7B. | Fux or radiant | "sari powerceraant Gus oFsouee| au? TyqMPLeT®]| © [ML? T+] intensity a Lumi ; 79. | luminous Fix of || mos erergy ented ML? TY/ET] source we [M] - Mass [L] - Length [7] Dimensions help us to check the correctness of equations. — Time [K]-Temperature [A] - Electric current [mol] - Amount of substance del Higenordi dist ale ee OF ee ca i i Relationship with ey aie S.No | Physical quantity other physical quantities Dimensions Dimensional formula Luminous intensity or L 27-4 80. illuminating pein: of aninous fl IML" T "1 [ML?T*] souce lid angle [M°L° T°] Intensity of Lumi i i a 81. illumination or Srlnows Intensity (ML* T*)/(L7] [ML°T™] luminance (distance) 82. Relative luminosity ae og ot (ML? T~'] [M°L°T?] luminous flux of peak sensitivit [ML Tt] wavelength (555 nm) source of same power 83. Luminous efficienc Total luminous flux ML? 77] /(ML2T* M°L°T? 4 Total radiant flux t POETS t ] 84, Tlluminance or Luminous flux incident —_— bak illumination area (ML*T“]/[L*] [ML°T™'] 85. Mass defect cia” te nadie of a al [M] [ML°T?] 86. Binding energy of Mass defect x (speed of light (M][LT7*]? [ML? T~2] nucleus in vacuum)? 87. Decay constant 0.693/half life sa | [M°L°T] 88. Resonant frequency (iiduciance:s capacitance) "2 [ML? Te Ay [M°L° Ao T"!] [Mt L qT? A i 89. Quality factor or Q- Resonant frequency x inductance | [T7'] [ML?T* A7] [M°L°T°] factor of coil Resistance [ML? T3 A? ] 90. | Power of lens (Focal length)* (L] [M°L* T°] 91, Magnification Image distance LI/TL Groin: Object distance (LJ/0L] [M°L*T*] 92. Fluid flow rate (1/8) (pressure) (radius)* [ML‘T~*] [L*] [M°L'T"] (viscosity coefficient) x (length) (ML*T*] [L] 93. Capacitive reactance (Angular frequency x cr yoMte2rtay [ML?T-? A-2] capacitance)! 94. Inductive reactani (Angular frequency x ty ry? 7-2 po? 27-3 9-2 ee faduickarta) (T*)(ML? TT? A?) [ML?T? A?) yp Dimensions help us to check the correctness of equations. [M] - Mass [L] - Length (T] - Time [K]- Temperature [A] - Electric current [mol]- Amount of substance | _ 
