Physics - Grade XI or Standard XI
Dimensions and Dimensional Equations
Symbols for Dimensions:
Following symbols are used to denote the dimensions:
L - length, M - mass, T - time, K - temperature, I - current, C - luminous intensity, mol - amount of substance.
Dimensions of a physical quantity:
The dimensions of a physical quantity are the powers to which fundamental units must be raised in order to obtain the unit of a given physical quantity.
Dimensional equation:
An expression, which gives the relation between the derived units and fundamental units in terms of dimensions is called a dimensional equation.
Example of dimensional equations:
Dimensional equation for force = [L1 M1 T-2].
| Quantity | Formula Short | Dimensional Equation | SIU |
|---|---|---|---|
| Length | L = Length | [M0 L1 T0] | m |
| Mass | M = Mass | [M1 L0 T0] | kg |
| Time | T = Time | [M0 L0 T1] | s |
| Electric Current | I = Electric Current | [M0 L0 T0 I1] | A (ampere) |
| Area | A = L2 | [M0 L2 T0] | m2 |
| Volume | V = L3 | [M0 L3 T0] | m3 |
| Density | ρ = m / V | [M1 L-3 T0] | kg/m3 |
| Velocity | v = L / T | [M0 L1 T-1] | m/s |
| Acceleration | a = L / T2 | [M0 L1 T-2] | m/s2 |
| Gravitational acceleration | g = a | [M0 L1 T-2] | m/s2 |
| Momentum | p = mv | [M1 L1 T-1] | kg.m/s |
| Force | f = ma | [M1 L1 T-2] | N (newton) |
| Impulse | J = ft | [M1 L1 T-1] | N.s |
| Work | W = fs | [M1 L2 T-2] | J (joule) |
| Kinetic Energy | KE = W2 | [M1 L2 T-2] | J (joule) |
| Gravitational Potential Energy | U = mgh | [M1 L2 T-2] | J (joule) |
| Energy | Energy = Work | [M1 L2 T-2] | J (joule) |
| Power | P = U/t | [M1 L2 T-3] | W (watt) |
| Pressure | Pressure = force / area | [M1 L-1 T-2] | Pa (pascal) |
| Weight | Weight = force | [M1 L1 T-2] | N (newton) |
| Weight | Weight = mass x g | [M1 L1 T-2] | N (newton) |
| Heat | Heat = Work = Energy | [M1 L2 T-2] | J (joule) |
| Electric Charge | q = It | [M0 L0 T1 I1] | C (coulomb) |
| Electric Field Intensity | E = force / charge | [M1 L1 T-3 I-1] | N/C |
| Electric Potential | V = E x r | [M1 L2 T-3 I-1] | V (volt) |
| Resistance | R = V / I | [M1 L2 T-3 I-2] | Ω (ohm) |
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