If a scientist is comparing the energy output of two light bulbs and records their values in joules, which dimensional formula should be used to represent energy in the SI system?
\([M L^2 T^{-2}]\)
Energy is defined as the capacity to do work, and work is force multiplied by displacement.
Force has the dimensional formula \([M L T^{-2}]\), so work (and hence energy) is \([M L T^{-2}] \times [L] = [M L^2 T^{-2}]\).
This matches the joule, the SI unit of energy, confirming the dimensional formula is unique among the given options.
Hence, the correct dimensional formula for energy is \([M L^2 T^{-2}]\).
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