Question

The SI unit of energy J= kg m^2 s^-2 ,that of speed v 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 v^3
b. K=(1/2) mv^2
c. K=ma
d.K=(3/16) mv^2
K=(1/2) mv^2 + ma

Answer 1

The answer is c. K=ma
ma =mv/t which does not match with the dimensions ok K

Answer 2

K=(1/2) mv^2 is the formulae for kinetic energy (K).

Explanation:

In Order to test the dimensional consistency, the required conditions are:

i). Each equation or formulae should have similar dimensions on the equation's both sides.

The proportions of an equation for kinetic energy on L.H.S. would be

{k} = {$ML^{2} T^{-2}$}

Thus, the dimensions on R.H.S. would be K=(1/2) mv^2 as it correctly goes with the definition of kinetic energy.

Learn more: SI unit of energy

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