Physics - Unit & Dimension Question with Solution | TestHub

The dimensions of Planck constant, $[h]=\left[\frac{E}{v}\right]=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$ Force, $[F]=\left[{\mathrm{MLT}}^{-2}\right]$ Displacement, $[d]=[\mathrm{L}]$ Time $[t]=[\mathrm{T}]$ $\therefore$ $$[F][d][t]=\left[{\mathrm{MLT}}^{-2}\right][\mathrm{L}][\mathrm{T}]$$ $$=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$$ Hence the dimensions of Planck's constant is the same as the product of force, displacement and time.