Application of Dimensional Formula of Energy

The dimensional formula of energy, [ML²T^-2], is crucial in various applications in physics, particularly in checking the dimensional consistency of equations and deriving relationships between physical quantities.

For example, when dealing with kinetic energy, which is given by the formula:

K.E. = (1/2)mv²

Here, mass (m) has the dimensional formula [M], and velocity (v) has the dimensional formula [LT^-1]. Substituting these into the kinetic energy formula, we get:

K.E. = (1/2) × [M] × [LT^-1]² = [M] × [L²T^-2] = [ML²T^-2]

This confirms that the dimensional formula of kinetic energy is consistent with that of energy. Thus, dimensional analysis helps verify that our equations are dimensionally correct, ensuring their physical validity.