Rule out or accept the following formulae for kinetic energy on the basis of dimensional arguments:(i) 3/16mv^2 (ii) 1/2mv^2+ma

Question

Rule out or accept the following formulae for kinetic energy on the basis of dimensional arguments:

(i) \(\frac{3}{16}mv^2\)

(ii) \(\frac{1}{2}mv^2+ma\)

Answer 1

Dimensions of K.E.= [ML²T^-2]

Dimensions of \(\frac{3}{16}mv^2\) = [M][LT^-1]² = [ML²T^-2]

Dimensions of \(\frac{1}{2}mv^2+ma\) = [ML²T^-2] + [MLT^-2]

So, (ii) formula is incorrect as its dimensions are different from the dimensions of kinetic energy.