Physics > Unit and Dimensions > 8.0 Dimensional formula
Unit and Dimensions
1.0 Introduction
2.0 Physical quantity
3.0 SI units
3.1 Definition of standard units
3.2 System of units
3.3 Rules for writing units
3.4 Characteristics of a standard unit
3.5 Advantages of SI
4.0 SI prefixes
5.0 Conversion of units
6.0 Important practical units
7.0 Dimensions
8.0 Dimensional formula
9.0 Dimensional equation
10.0 List of dimensional formula
11.0 Application of dimensional analysis
11.1 To check the dimensional consistency of equations
11.2 To deduce relation among the physical quantities
11.3 To convert one system of unit into another system of unit
12.0 Limitations of dimensional analysis
8.1 Physical quantities having same dimensional formulae
3.2 System of units
3.3 Rules for writing units
3.4 Characteristics of a standard unit
3.5 Advantages of SI
11.2 To deduce relation among the physical quantities
11.3 To convert one system of unit into another system of unit
| S.No. | Physical quantities | Dimensional formula |
| 1. | Frequency, angular frequency, angular velocity, velocity gradient | $\left[ {{M^0}{L^0}{T^{ - 1}}} \right]$ |
| 2. | Work internal energy, potential energy, kinetic energy, torque, moment of force | $\left[ {{M}{L^2}{T^{ - 2}}} \right]$ |
| 3. | Pressure, stress, Young's modulus, bulk modulus, modulus of rigidity, energy density | $\left[ {{M}{L^{-1}}{T^{ - 2}}} \right]$ |
| 4. | Momentum and impulse | $\left[ {{M}{L}{T^{ - 1}}} \right]$ |
| 5. | Acceleration, Acceleration due to gravity, gravitational field intensity | $\left[ {{M^0}{L}{T^{ - 2}}} \right]$ |
| 6. | Thrust, force, weight, energy gradient | $\left[ {{M}{L}{T^{ - 2}}} \right]$ |
| 7. | Angular momentum and Planck's constant $(h)$ | $\left[ {{M}{L^2}{T^{ - 1}}} \right]$ |
| 8. | Surface tension, force gradient, spring constant | $\left[ {{M}{L^0}{T^{ - 2}}} \right]$ |
| 9. | Strain, refractive index, relative density, angle, solid angle, distance gradient, relative permeability, relative permittivity | $\left[ {{M^0}{L^0}{T^{0}}} \right]$ |
| 10. | If $P$ is pressure, $V$ is volume, $m$ is mass, $s$ is specific heat, $L$ is latent heat, $\Delta T$ is rise in temperature then $PV$, $mL$, $(ms \Delta T)$ all have dimensions of energy | $\left[ {{M}{L^2}{T^{ - 2}}} \right]$ |
| 11. | If $l$ is length, $g$ is acceleration due to gravity, $m$ is mass, $k$ is force constant, $R$ is radius of earth, then ${\left( {\frac{l}{g}} \right)^{\frac{1}{2}}},{\left( {\frac{m}{k}} \right)^{\frac{1}{2}}},{\left( {\frac{R}{g}} \right)^{\frac{1}{2}}}$ all have the dimensions of time | $\left[ {{M^0}{L^0}{T}} \right]$ |
