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

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.

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

i think the answer is a, hope this is right, that would be my best guess.