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The SI unit of energy is \( J=k g \mathrm{~m}^{2} \mathrm{~s}^{-2} \) that of speed \( \mathrm{v} \) is \( \mathrm{ms}^{-1} \) and of acceleration a is \( \mathrm{ms}^{-2} \). Which of the formulae for kinetic energy ( \( \mathrm{K} \) ) given below can you rule out on the basic of dimensional arguments ( \( \mathrm{m} \) stands for the mass of the body)
I. \( \mathrm{K}=\mathrm{m}^{2} \mathrm{v}^{2} \)
II. \( \mathrm{K}=(1 / 2) \mathrm{mv}^{2} \)
III. \( \mathrm{K}=\mathrm{ma} \)
IV. \( \mathrm{K}=(3 / 16) \mathrm{mv}^{2} \)
\( \mathrm{V} . \mathrm{K}=\left(\frac{1}{2}\right) \mathrm{mv} \mathrm{v}^{2}+\mathrm{ma} \)
a. I and II
b. Only II
c. II and IV
d. I, III and V
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