If two quantities have same dimensions do they represent same physical content?
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In general, if the dimensions are same, the quantities do represent the same physical content. Like work and energy have the same dimensions and represent inter-convertible quantity. They perhaps do not represent the same physical content. ... These two quantities represent the same quantity - same meaning and content.
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Generally it happen but not always. for example the angular moment is given by strenght per arm (N x m) is phisically different by Work or Energy that has the same dimension, that is expressed in Joule (J= N x m)
Also concentation (g/L) can has the dimension of density (g/L) but the first is g of solute while the second is g of solution.
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