Dimensional Analysis Of Energy

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A teacher writes the kinetic energy expression for a moving ball and asks students to confirm its dimensions before solving a numerical problem. What is the dimensional formula of kinetic energy?

RankGuru · Accepted Answer

Per NCERT Class 11, Chapter 2 (Units and Measurements), the dimensions of any energy term can be obtained from its formula. Kinetic energy is given by (1/2) m v^2, where the numerical factor one half is dimensionless. Mass m carries [M^{1}] and velocity v carries [L^{1}T^{-1}], so v^2 carries [L^{2}T^{-2}]. Multiplying mass and the squared velocity gives [M^{1}][L^{2}T^{-2}] = [M^{1}L^{2}T^{-2}]. The option [M^{1}L^{1}T^{-2}] is wrong because it matches force, not energy. The option [M^{1}L^{2}T^{-1}] is wrong as it corresponds to angular momentum. The option [M^{1}L^{2}T^{-3}] is wrong since it represents power, which is energy per unit time. A final check confirms that work, which equals force times displacement, also gives [M^{1}L^{1}T^{-2}][L^{1}] = [M^{1}L^{2}T^{-2}], matching kinetic energy as required by the work-energy theorem.

Dimensional Analysis Of Energy

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