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13 April, 14:40

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

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  1. 13 April, 14:57
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    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.
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