All Dimensional Formula List PDF Download

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All Dimensional Formula List PDF Download

FilenameAll Dimensional Formula List
PDF Size200 KB
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All Dimensional Formula List PDF

Dimensional Formula : An expression along with power of mass, length & time which indicates how physical quantity depends upon fundamental physical quantity.

e.g. Speed = Distance/Time

= [ML1 T-1]

It tells us that speed depends upon L & T. It does not depends upon M.

Dimensional Equation : An equation obtained by equating the physical quantity with its dimensional formula is called dimensional equation.

The dimensional equation of area, density & velocity are given as under

Area = [ML2 T]
Density = [M1L-3T0]
Velocity = [M0L1T-1]

Dimensional formula SI& CGS unit of Physical Quantities

Sl. NoPhysical QuantityFormulaDimensional FormulaS.I Unit
1Area (A)Length x Breadth[M0L2T0]m2
2Volume (V)Length x Breadth x Height[M0L3T0]m3
3Density (d)Mass / Volume[M1L-3T0]kgm-3
4Speed (s)Distance / Time[M0L1T-1]ms-1
5Velocity (v)Displacement / Time[M0L1T-1]ms-1
6Acceleration (a)Change in velocity / Time[M0L1T-2]ms-2
7Acceleration due to gravity (g)Change in velocity / Time[M0L1T-2]ms-2
8Specific gravityDensity of body/density of water at 4oCNo dimensions [M0L0T-0]No units
9Linear momentum (p)Mass x Velocity[M1L1T-1]kgms-1
10Force (F)Mass x Acceleration[M1L1T-2]N
11Work (W)Force x Distance[M1L2T-2]J (Joule)
12Energy (E)Work[M1L2T-2]J
13Impulse (I)Force x Time[M1L1T-1]Ns
14Pressure (P)Force / Area[M1L-1T-2]Nm-2
15Power (P)Work / Time[M1L2T-3]W
16Universal constant of gravitation (G)\large\begin{aligned}\frac{Force \times (distance)^{2}}{(mass)^{2}}\end{aligned}[M-1L3T-2]Nm2kg-2
17Moment of inertia (I)Mass x (distance)2[M1L2T0]kgm2
18Moment of force, moment of coupleForce x distance[M1L2T-2]Nm
19Surface tension (T)Force / Length[M1L0T-2]Nm-1
20Surface energy (E)Energy / unit area[M1L0T-2]Nm-1
21Force constant (x)Force / Displacement[M1L0T-2]Nm-1
22Coefficient of viscosity ( η )\large\begin{aligned}\frac{Force}{area\times velocity\;gradient}\end{aligned}[M1L-1T-1]Nsm-2
23Thrust (F)Force[M1L1T-2]N
24Tension (T)Force[M1L1T-2]N
25StressForce / Area[M1L-1T-2]Nm-2
26StrainChange in dimension / Original dimensionNo dimensions [M0L0T-0]No unit
27Modulus of Elasticity (E)Stress / strain[M1L-1T-2]Nm-2
28Radius of gyration (k)Distance[M0L1T0]m
29Angle ( θ), Angular displacementArc length / RadiusNo dimensions [M0L0T-0]rad
30Trigonometric ratio ( sin θ, cos θ, tan θ, etc)Length / lengthNo dimensions [M0L0T-0No unit
31Angular velocity( ω )Angle / Time[M0L0T-1]rad s-1
32Angular acceleration( α )Angular velocity / Time[M0L0T-2]rad s-2
33Angular momentum (J)Moment of inertia x Angular velocity[M1L2T-1]kgm2s-1
34Torque (????)Moment of inertia x Angular acceleration[M1L2T-2]Nm
35Velocity gradient \large \begin{aligned} \left ( \frac{dv}{dx} \right ) \end{aligned}Velocity / Distance[M0L0T-1]s-1
36Rate flowVolume / Time[M0L3T-1]m3s-1
37Wavelength( ???? )Length of a wavelet[M0L1T0]m
38Frequency(\large \begin{aligned} \nu \end{aligned})Number of vibrations/second or 1/time period[M0L0T-1]Hz or s-1
39Angular frequency (ω)2π x frequency[M0L0T-1]
40Planck’s constant (h)Energy / Frequency[M1L2T-1]Js
41Buoyant forceForce[M1L1T-2]N
42Relative densityDensity of substance / density of water at 4oCNo dimensions [M0L0T-0]No unit
43Pressure gradientPressure / Dstance[M1L-2T-2]Nm-3
44Pressure energyPressure x Volume[M1L2T-2]J
46Heat (Q)Energy[M1L2T-2]J
47Latent heat (L)Heat / Mass[M0L2T-2]Jkg-1
48Specific heat (S)\begin{aligned} \frac{Heat}{Mass\times temperature}\end{aligned}[M0L2T-2K-1]Jkg-1K-1
49Thermal expansion coefficient or thermal expansivity\begin{aligned}\frac{Change\;in\;dimension}{original\;dimension\times temperature}\end{aligned}[M0L0T0K-1]K-1
50Thermal conductivity\begin{aligned}\frac{Heat\;energy\times thickness}{Area\times temperature\times time}\end{aligned}[M1L1T-3K-1]Wm-1K-1
51Bulk modulus or (compressibility)-1\begin{aligned}\frac{Volume\times (change\;in\;pressure)}{(change\;in\;volume)}\end{aligned}[M1L-1T-2]Nm-2 or Pascals
52Centripetal acceleration\begin{aligned}\frac{(velocity)^2}{radius}\end{aligned}[M0L1T-2]
53Stefan constant (σ)\begin{aligned}\frac{(Energy / area \times time)}{(temperature)^4}\end{aligned}[M1L0T-3K-4]Wm−2K−4 
54Wien constantWavelength X temperature[M0L1T0K1]mK
55Gas constant (R)\begin{aligned} \frac{Pressure \times Volume}{Temperature}\end{aligned}[M1L2T-2K-1]JK-1
56Boltzmann constant (K)Energy / temperature[M1L2T-2K-1]JK-1
57Charge (q)Current x time[M0L0T1A1]C
58Current densityCurrent / area[M0L-2T0A1]A m−2
59Electric potential (V), voltage, electromotive forceWork / Charge[M1L2T–3A-1]V
60Resistance (R)Potential difference / Current[M1L2T–3A-2]ohms (Ω)
61CapacitanceCharge / potential difference[M1L2T4A2]F (Farad)
62Electrical resistivity or (electrical conductivity)-1\begin{aligned}\frac{Resistance \times area}{length}\end{aligned}[M1L3T-3A2]Ωm ( resistivity)
63Electric field (E)Force / Charge[M1L1T-3A-1]NC-1
64Electric fluxElectric field X area[M1L3T3A-1]Nm2C-1
65Electric dipole momentTorque / electric field[M0L1T1A1]C m
66Electric field strength or electric intensityPotential difference / distance[M1L1T-3A-1]NC-1
67Magnetic field (B), magnetic flux density, magnetic induction\begin{aligned}\frac{Force}{current \times length}\end{aligned}[M1L0T-2A-1]T (Tesla)
68Magnetic flux (Φ)Magnetic field X area[M1L2T-2A-1]Wb (Weber)
69InductanceMagnetic flux / current[M1L2T-2A-2]H (Henry)
70Magnetic dipole momentTorque /field
current X area
71Magnetic field strength (H), magnetic intensity or magnetic moment densityMagnetic moment / volume[M0L-1T0A1]Am-1
72Hubble constantRecession speed / distance[M0L0T-1]s-1
73Intensity of wave(Energy/time)/area[M1L0T-3]Wm-2
74Radiation pressureIntensity of wave / speed of light[M1L1T-2]
75Energy densityEnergy / volume[M1L-1T-2]Jm-3
76Critical velocity\begin{aligned}\frac{Reynold's\;number \times coefficient\;of\;viscocity}{Mass\; density \times radius}\end{aligned}[M0L1T-1]ms-1
77Escape velocity\begin{aligned}(2 \times acceleration\;due\;to\;gravity\times earth's\;radius)^{1/2}\end{aligned}[M0L1T-1]ms-1
78Heat energy, internal energyWork ( = Force X distance)[M1L2T-2]J
79Kinetic energy\begin{aligned}\frac{1}{2}mass \times (velocity)^{2}\end{aligned}[M1L2T-2]J
80Potential energyMass X acceleration due to gravity X height[M1L2T-2]J
81Rotational kinetic energy\begin{aligned}\frac{1}{2}\times moment\;of\;inertia\times (angular\;velocity)^{2}\end{aligned}[M1L2T-2]J
82Efficiency\begin{aligned}\frac{output\;work\;or\;energy}{input\;work\;or\;energy}\end{aligned}No dimensions [M0L0T0]No unit
83Angular impulseTorque X time[M1L2T-1]Js (Joule second)
84Permitivity constant (of free space)\begin{aligned}\frac{Charge \times charge}{4\pi\times electric\;force\times (distance)^{2} }\end{aligned}[M-1L-3T4A2]F m-1
85Permeability constant (of free space)\begin{aligned}\frac{2\pi \times force\times distance}{current\times current\times length}\end{aligned}[M1L1T-2A-2]NA-2
86Refractive index\begin{aligned}\frac{Speed\;of\;light\;in\;vacuum}{Speed\;of\;light\;in\;medium}\end{aligned}No  dimensions [M0L0T0]No unit
87Faraday constant (F)Avogadro constant X elementary charge[M0L0T1Amol-1]C mol-1
88Wave number\begin{aligned}\frac{2\pi }{wavelength}\end{aligned}[M0L-1T0]
89Radiant flux, Radiant powerEnergy emitted / time[M1L2T-3]W(Watt)
90Luminosity of radiant flux or radiant intensity\begin{aligned}\frac{Radiant\;power\;or\;radiant\;flux\;of\;source}{Solid\;angle}\end{aligned}[M1L2T-3]W sr-1 (Watt/steradian)
91Luminous power or luminous flux of source\begin{aligned}\frac{Luminous\;energy\;emitted}{time}\end{aligned}[M1L2T-3]lm (lumen)
92Luminous intensity or illuminating power of sourceLuminous flux / Solid angle[M1L2T-3]cd (candela)
93Intensity of illumination or luminance (Lv)\begin{aligned}\frac{Luminous\;intensity}{(distance)^{2}}\end{aligned}[M1L0T-3]cd m-2
94Relative luminosityLuminous flux of a source of given wavelength / luminous flux of peak sensitivity wavelength(555 nm) source of the same powerNo dimensions [M0L0T0]No unit
95Luminous efficiencyTotal luminous flux / Total radiant fluxNo dimensions [M0L0T0]No unit
96Illuminance or illuminationLuminous flux incident / Area[M1L0T-3]lx (lux)
97Mass defect(Sum of masses of nucleons) – (mass of the nucleus)[M1L0T0]
98Binding energy of nucleus\begin{aligned}Mass\;defect\times (Speed\;of\;light\;in\;vacuum)^{2}\end{aligned}[M1L2T-2]
99Decay constant0.693 / half-life[M0L0T-1]
100Resonant frequency\begin{aligned}(Inductance\times capacitance)^{-1/2}\end{aligned}[M0L0T-1A0]
101Quality factor or Q-factor of coil\begin{aligned}\frac{Resonant\;frequency \times inductance}{Resistance}\end{aligned}No dimensions [M0L0T0]No unit
102Power of lens\begin{aligned}\frac{1}{focal\;length}\end{aligned}[M0L-1T0]D (dioptre)
103MagnificationImage distance / Object distanceNo dimensions [M0L0T0]No unit
104Fluid flow rate\begin{aligned}\frac{(\pi /8)(pressure)\times (radius)^{4}}{Viscosity\;coefficient\times length}\end{aligned}[M0L3T-1]m3s-1
105Capacitive reactance (Xc)(Angular frequency X capacitance)-1[M1L2T-3A-2]ohms (Ω)
106Inductive reactance (XL)(Angular frequency X inductance)[M1L2T-3A-2]ohms (Ω)

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