The SI unit of energy is `J = kg m^2 s^(-2),` that of speed `upsilon` is `ms^(-1)` and of acceleration a is `ms^(-2)` which of the formulae for kinetic energy (K) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body).
(a) `K = m^2 upsilon^3` (b) `K = (1)/(2)m upsilon^2` (c ) K= ma
(d) `K =(3)/(16)m upsilon^2` (e ) `K = (1)/(2) m upsilon^2 +ma`

Explanation

To determine which formula for kinetic energy (K) can be ruled out based on dimensional analysis, we will analyze each given formula step by step.

### Given Information:
- SI unit of energy (K) is Joule (J) = kg m² s⁻²
- SI unit of speed (ν) is m s⁻¹
- SI unit of acceleration (a) is m s⁻²

### Dimensional Analysis:
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