Question

if force(F),length(L) and time(T) are chosen as the fundamental quantities, then what would be the dimensional formula for density?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Density}=\frac{\mathrm{mass}}{\mathrm{volume}} \\ \mathrm{dimensional}\mathrm{formula}\mathrm{of}\mathrm{volume}=\left[{\mathrm{L}}^3\right] \\ \mathrm{we}\mathrm{know}\mathrm{that}, \\ \mathrm{mass}=\frac{\mathrm{force}}{\mathrm{acceleration}} \\ \mathrm{dimensional}\mathrm{formula}\mathrm{of}\mathrm{acceleration}=\left[{\mathrm{LT}}^{-2}\right] \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \mathrm{dimensional}\mathrm{formula}\mathrm{of}\mathrm{force}=\left[\mathrm{F}\right] \\ \mathrm{so},\mathrm{dimensional}\mathrm{formula}\mathrm{of}\mathrm{mass}=\frac{\left[\mathrm{F}\right]}{\left[{\mathrm{LT}}^{-2}\right]}=\left[{\mathrm{FL}}^{-1}{\mathrm{T}}^2\right] \\ \mathrm{Dimensional}\mathrm{formula}\mathrm{of}\mathrm{density}=\frac{\left[{\mathrm{FL}}^{-1}{\mathrm{T}}^2\right]}{\left[{\mathrm{L}}^3\right]} \\ \mathrm{Dimensional}\mathrm{formula}\mathrm{of}\mathrm{density}=\left[{\mathrm{FL}}^{-4}{\mathrm{T}}^2\right] \end{gathered}$$