Understanding Dimensional Formula of Energy

The dimensional formula of energy represents how energy can be expressed in terms of the basic physical dimensions: mass (M), length (L), and time (T). According to the NCERT syllabus, energy is defined as the capacity to do work. The standard unit of energy is the Joule (J).

The work done (or energy) is given by the formula:

Work (W) = Force (F) × Distance (d)

Force can be expressed as mass times acceleration (F = m × a). Hence,

W = m × a × d

We know that acceleration (a) has the dimensional formula [L T^-2]. Therefore,

W = m × [L T^-2] × d

Since distance (d) has the dimensional formula [L], we get:

W = m × L × L T^-2 = ML²T^-2

So, the dimensional formula of energy is [ML²T^-2].