A dimensional formula is a statement expressing a physical quantity in terms of its fundamental units with suitable dimensions. An example provided is the dimensional formula for Force.
According to the information, the dimensional formula for Force is:
[M L T^{-2}]
Specifically, it is stated as:
F = [M L T$^{-2}$]
This formula represents Force (F) in terms of the fundamental dimensions of Mass (M), Length (L), and Time (T).
Why is this the dimensional formula for Force?
The reason given relates to the units of Force.
- The standard unit of Force is the Newton (N).
- The Newton can also be expressed in terms of more fundamental units: kilogram * meter / second² (kg*m/s²).
Breaking this down by dimensions:
- Kilogram (kg) corresponds to the dimension of Mass (M).
- Meter (m) corresponds to the dimension of Length (L).
- Second (s) corresponds to the dimension of Time (T).
Since the unit is kg * m / s², or kg * m * s⁻², the corresponding dimensional formula is derived by replacing the units with their dimensions: M¹ L¹ T⁻². This simplifies to [M L T$^{-2}$].
Therefore, the dimensional formula for Force encapsulates how force depends on the fundamental quantities of mass, length, and time.
