The SI unit of energy is $J=kg{m}^2{s}^{-2},$ that of speed v is $m{s}^{-1}$ and of acceleration a is $m{s}^{-2}$ which one of the formula for kinetic energy given below is correct on the basis of dimensional arguments.

[Given m stands for the mass of body]

detailed solution

Correct option is D

Every correct formula or equation must have the same dimensions on both sides of the equation. Also, only quantities with the same physical dimensions can be added orsubtracted. The dimensions of the quantity on the right side for (a) is K=m2v2Putting, m=[M],v=[LT−1]∴  dimensions  are  [M2L2T−2]for (b), K =maputting m=[M],a=[LT−2]∴  dimensions  are  [MLT−2]option (c) has no proper dimensions,option (d), K=12mv2, putting m = [M]and V=[LT−1], we haveK=[M][LT−1]2=[ML2T−2]in units it is written as kg  m2s−2