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How to calculate dimensional formulae

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 Dimensional formula
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 Introduction


 Dimensional formula tells us which basic units are used to measure a unit.

 In dimensional formula,

 M - sign of mass

 L - sign of length

 T - time signal


 1. dimensional formula for area

 Area = Length × Breadth

 = L × L

 = L²

 Dimensional Formula:- M⁰L²T⁰

 m, s, and kg  are generally units of length, time, and mass.


 Extracting the dimensional formula from the unit:-


 1.Area- m²

 m² means L²

 Hence the dimensional formula:- M⁰L²T⁰


2. distance - m

 m means L¹

 Hence the dimensional formula:- M⁰L¹T⁰


 3.speed/velocity - m/s

 m/s i.e. L/T = L¹T⁻¹

 Hence the dimensional formula:- M⁰L¹T⁻¹

 4.Acceleration - m/s²


 m/s² i.e. L/T²= L¹T⁻²


 Hence the dimensional formula:- M⁰L¹T⁻²


 5.Momentum - kgm/s

 Kgm/s i.e. ML/T= M¹L¹T⁻¹

 Hence, the dimensional formula:- M¹L¹T⁻¹


6. Force - kg×m/s² ( mass × acceleration)

 Kg ×m/s²= M×L/T²

 = M¹L¹T⁻²


 7.Volume - m³

 M⁰L³T⁰


 All physical quantities whose SI unit is same, they have the same dimensional formula.

 Work

 kinetic energy

 heat

 potential energy


 The SI unit of all these is joule and their dimensional formula is also the same.


 work = force × distance


 = ma × distance


 = Kg × m/s² × distance


 =  M¹× L¹/T²×L


 = M¹L²T⁻²


 9) Dimensional formula for pressure


 pressure = force / area


 = ma/area


 = (Kg×m/s²)/m²


 = (M×L/T²)/L²


 = M¹L⁻¹T⁻²


 10) Dimensional formula for angular velocity


 Angular velocity = angle / time


 = (M⁰L⁰T⁰)/T¹


 = M⁰L⁰T⁻¹


 11) Dimensional formula for electric charge


 Electric charge =  current × time


 = A × T


 = M⁰L⁰T¹A¹


 12) Dimensional formula of power


 power = work/time


 = (force × distance)/time


 = (ma×distance)/time


 = (Kg×m/s²×m)/s


 = Kgm²/s³


 = ML²/T³


 = M¹L²T⁻³


 13) Dimensional formula for potential difference


 The work done on that charge in bringing a unit charge from infinity to a point is called potential difference.


 potential difference = work / charge


 = (force × distance)/(time × current)


 = (ma×distance)/(time × current)


 = (Kg×m/s²×m)/(s ×A)


 = (M×L/T²×L)/(T×A)


 = (M¹L²)/T³A¹


 = M¹L²T⁻³A⁻¹


 14) Dimensional formula of resistance


 R = V/I


 = (Work/charge)/current


 ={ (force × distance)/(current × time)}/current


 = {(ma ×L)/(A ×s)}/A


 = {(ma×L)/A²s


 = {(Kg×m/s²×L)}/A²s


 = Kgm×L/A²s³


 = M¹L¹×L/A²T³


 = M¹L²A⁻²T⁻³



 15) Dimensional formula of resistivity


 R =ρL/A


 = RA/L


 ={(M¹L²A⁻²T⁻³)L²}/L¹


 = M¹L³A⁻²T⁻³




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