Question

Each of the following equations was given by a student during an examination.

a)1/2mv2=1/2mv2+m2 gh
b)v=u+at2
c)ma=v2
Do the dimensional analysis of each equation and explain why the equations cannot be correct

Answer 1

Dimensional analysis is a procedure whereby fundamentals quantities in nature, and their units, called Fundamental units, are used to analyse the relationship between variables in a formula or equation to determine its accuracy.

The fundamental quantities and their units are:

Mass, M (kilogram, kg)

Length, L (metre, m)

Time, T (seconds, s)

For the equations to be dimensionally correct, all the variables in the equation must have the same dimension.

a) ½mv² = ½mv² + m²gh

v represents velocity, g represents accelerator due to gravity, h represents height.

M * (L / T)² = M * (L / T)² + M² * (L / T²) * L

ML² / T² = ML² / T² + M²L² / T²

The dimensions don't all match, hence, this equation cannot be correct.

b) v = u + at²

u represents velocity and a represents acceleration

L/T = L/T + (L/T²) * T²

L/T = L/T + L

The dimensions don't all match, hence, this equation cannot be correct.

c) ma = v2

M * L/T² = (L/T)²

ML/T² = L²/T²

The dimensions don't all match, hence, this equation cannot be correct.