Define Dimensions and write dimensions of Physical Quantities.
DIMENSION
In physics, the term Dimension is used to denote the qualitative nature of a physical quantity based on how the fundamental quantities are involved in its definition. Each basic fundamental quantity is assigned a specific dimensional symbol. The primary dimensions upon which mechanics is based are Mass [M], Length [L], and Time [T]. Representing a physical quantity in terms of these standard symbols highlights its core structural nature without regarding its numerical magnitude or unit choices.
DIMENSIONS OF PHYSICAL QUANTITIES
| S.No | Physical Quantity | Formula | Dimension | S.I Unit |
|---|---|---|---|---|
| 1 | Area | $\text{Length} \times \text{Breadth}$ | [L²] | $\text{m}^2$ |
| 2 | Volume | $\text{Length} \times \text{Breadth} \times \text{Height}$ | [L³] | $\text{m}^3$ |
| 3 | Density | $\text{Mass} / \text{Volume}$ | [ML⁻³] | $\text{kg}\cdot\text{m}^{-3}$ |
| 4 | Speed or Velocity | $\text{Distance} / \text{Time}$ | [LT⁻¹] | $\text{m}\cdot\text{s}^{-1}$ |
| 5 | Acceleration | $\text{Velocity} / \text{Time}$ | [LT⁻²] | $\text{m}\cdot\text{s}^{-2}$ |
| 6 | Force | $\text{Mass} \times \text{Acceleration}$ | [MLT⁻²] | $\text{kg}\cdot\text{m}\cdot\text{s}^{-2} = \text{N}$ |
| 7 | Pressure | $\text{Force} / \text{Area}$ | [ML⁻¹T⁻²] | $\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2} = \text{Pa}$ |
| 8 | Momentum | $\text{Mass} \times \text{Velocity}$ | [MLT⁻¹] | $\text{kg}\cdot\text{m}\cdot\text{s}^{-1}$ |
| 9 | Work | $\text{Force} \times \text{Displacement}$ | [ML²T⁻²] | $\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2} = \text{J}$ |
| 10 | Energy | $\text{Capacity to do Work}$ | [ML²T⁻²] | $\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2} = \text{J}$ |
| 11 | Power | $\text{Work} / \text{Time}$ | [ML²T⁻³] | $\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3} = \text{W}$ |
| 12 | Gravitational Constant ($G$) | $(\text{Force} \times \text{Distance}^2) / \text{Mass}^2$ | [M⁻¹L³T⁻²] | $\text{kg}^{-1}\cdot\text{m}^3\cdot\text{s}^{-2}$ |
| 13 | Torque or Couple | $\text{Force} \times \text{Perpendicular Distance}$ | [ML²T⁻²] | $\text{N}\cdot\text{m}$ |
| 14 | Angular Momentum | $\text{Mass} \times \text{Velocity} \times \text{Radius}$ | [ML²T⁻¹] | $\text{kg}\cdot\text{m}^2\cdot\text{s}^{-1}$ |
| 15 | Angle ($\theta$) | $\text{Arc Length} / \text{Radius}$ | Dimensionless | $\text{rad}$ |
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