Dimensional Formula for Various Quantities
The table below provides Dimensional Formulas for different physical quantities:
|
Physical Quantity |
Unit |
Dimensional Formula |
|---|---|---|
|
Acceleration or Acceleration due to Gravity |
ms-2 |
LT-2 |
|
rad |
M0L0T0 |
|
|
Angular Impulse |
Nms |
ML2T-1 |
|
rads-1 |
T-1 |
|
|
Angle (Arc/Radius) |
rad |
M0L0T0 |
|
Angular Frequency (Angular Displacement/Time) |
rads-1 |
T-1 |
|
kgm2s-1 |
ML2T-1 |
|
|
JK-1 |
ML2T-2θ– |
|
|
N/m2 |
ML-1T-2 |
|
|
Calorific Value |
JKg-1 |
L2T-2 |
|
Coefficient of Surface Tension (Force/Length) |
N/m |
MT-2 |
|
Coefficient of Linear or Areal or Volume Expansion |
K-1 |
θ-1 |
|
Coefficient of Thermal Conductivity |
Wm-1K-1 |
MLT-3θ-1 |
|
Compressibility (1/Bulk Modulus) |
m2N-2 |
M-1LT2 |
|
Density (Mass / Volume) |
Kg/m3 |
ML-3 |
|
Displacement, Wavelength, Focal Length |
m |
L |
|
Electric Capacitance (Charge/Potential) |
farad |
M-1L-2T4I2 |
|
Electric Conductivity (1/Resistivity) |
Sm-1 |
M-1L-3T3I2 |
|
ampere |
I |
|
|
Electric Field Strength or Intensity of Electric Field (Force/Charge) |
NC-1 |
MLT-3I-1 |
|
Emf (or) Electric Potential (Work/Charge) |
volt |
ML2T-3I-1 |
|
Energy Density (Energy/Volume) |
Jm-3 |
ML-1T-2 |
|
Electric Conductance (1/Resistance) |
Ohm-1 |
ML-1T-2T3I2 |
|
Electric Charge or Quantity of Electric Charge |
coulomb |
IT |
|
Cm |
LTI |
|
|
Electric Resistance (Potential Difference/Current) |
ohm |
ML2T-3I-2 |
|
Energy (Capacity to do work) |
joule |
ML2T-2 |
|
Entropy |
Jθ–1 |
ML2T-2θ-1 |
|
newton (N) |
MLT-2 |
|
|
Frequency (1/period) |
Hz |
T-1 |
|
Force Constant or Spring Constant (Force/Extension) |
Nm-1 |
MT-2 |
|
Gravitational Potential (Work/Mass) |
J/kg |
L2T-2 |
|
Heat (Energy) |
J or calorie |
ML2T-2 |
|
Illumination (Illuminance) |
lumen/m2 |
MT-3 |
|
Inductance |
henry (H) |
ML2T-2I-2 |
|
Intensity of Magnetization (I) |
Am-1 |
L-1I |
|
Impulse |
Ns |
MLT-1 |
|
Intensity of Gravitational Field (F/m) |
Nkg-1 |
LT-2 |
|
Joule’s Constant |
Jcal-1 |
M0L0To |
|
Latent Heat (Q = mL) |
Jkg-1 |
L2T-2 |
|
Luminous Flux |
Js-1 |
ML2T-3 |
|
Linear density (mass per unit length) |
Kgm-1 |
ML-1 |
|
Magnetic Dipole Moment |
Am2 |
L2I |
|
Magnetic induction (F = Bil) |
NI-1m-1 |
MT-2I-1 |
|
Modulus of Elasticity (Stress/Strain) |
Pa |
ML-1T-2 |
|
Momentum |
kgms-1 |
MLT-1 |
|
weber (Wb) |
ML2T-2I-1 |
|
|
Magnetic Pole Strength |
Am (ampere–meter) |
LI |
|
Kgm2 |
ML2 |
|
|
Planck’s Constant (Energy/Frequency) |
Js |
ML2T-1 |
|
Power (Work/Time) |
watt (W) |
ML2T-3 |
|
Pressure Coefficient or Volume Coefficient |
θ-1 |
θ-1 |
|
Permittivity of Free Space |
Fm-1 |
M-1L-3T4I2 |
|
Poisson’s Ratio (Lateral Strain/Longitudinal Strain) |
Dimensionless |
M0L0T0 |
|
Pressure (Force/Area) |
N/m2 |
ML-1T-2 |
|
Pressure Head |
m |
L |
|
disintegrations per second |
T-1 |
|
|
Dimensionless |
M0L0T0 |
|
|
Specific Conductance or Conductivity (1/Specific Resistance) |
Sm-1 |
M-1L-3T3I2 |
|
Specific Gravity (Density of the Substance/Density of Water) |
Dimensionless |
M0L0T0 |
|
Specific Volume (1/Density) |
m3kg-1 |
M-1L3 |
|
Stress (Restoring Force/Area) |
N/m2 |
ML-1T-2 |
|
Ratio of Specific Heats |
Dimensionless |
M0L0T0 |
|
Resistivity or Specific Resistance |
Ω-m |
ML3T-3I-2 |
|
Specific Entropy (1/entropy) |
KJ-1 |
M-1L-2T2θ |
|
Specific Heat (Q = mst) |
L2T-2θ-1 |
|
|
Speed (Distance/Time) |
m/s |
LT-1 |
|
Strain (Change in Dimension/Original dimension) |
Dimensionless |
M0L0T0 |
|
Surface Energy Density (Energy/Area) |
J/m2 |
MT-2 |
|
Temperature |
θ |
θ |
|
Thermal Capacity |
Jθ-1 |
ML2T-2θ-1 |
|
Nm |
ML2T-2 |
|
|
Temperature Gradient |
θm-1 |
L-1θ |
|
Time Period |
second |
T |
|
Universal Gas Constant (Work/Temperature) |
Jmol–1θ-1 |
ML2T-2θ-1 |
|
Universal Gravitational Constant |
Nm2kg-2 |
M-1L3T-2 |
|
Velocity (Displacement/Time) |
m/s |
LT-1 |
|
Volume |
m3 |
L3 |
|
Velocity Gradient (dv/dx) |
s-1 |
T-1 |
|
Water Equivalent |
kg |
M |
|
J |
ML2T-2 |
|
|
Decay Constant |
s-1 |
T-1 |
|
J |
ML2T-2 |
|
|
J |
ML2T-2 |
Dimensional Formula
Dimensional Formulas play an important role in converting units from one system to another and find numerous practical applications in real-life situations. Dimensional Formulas are a fundamental component of the field of units and measurements. In mathematics, Dimension refers to the measurement of an object’s size, extent, or distance in a specific direction, such as length, width, or height, but in the context of physical quantities, the dimension signifies the exponent to which fundamental units must be raised to yield a single unit of that specific quantity.
In this article, we will discuss the introduction, definition, properties, and limitations of a Dimensional Formula and its meaning. We will also understand dimensional formulas for different physical quantities and Dimensional equations. We will also solve various examples and provide practice questions for a better understanding of the concept of this article. We have to study Dimensional Formula in Class 11.
Table of Content
- What is Dimensional Formula?
- Dimensional Formula for Various Quantities
- Application of Dimensional Formula
- Limitations of Dimensional Formula
- Dimensional Formula and Dimensional Equations