Question

If two quantities have same dimensions ,do they represent same physical content? And how can force and energy density have same dimensions

Answer 1

They need not always represent the same physical content.

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.


dimension of energy density ---- ML^-1T^-2


dimension of force --- MLT^-2]