Question

deduce the dimensional formula for the following quantities from their definitions
1 momentum
2 moment of force
3 work
4 power

Answer 1

$$\begin{gathered} \mathrm{Momentum}:\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{mass}\mathrm{and}\mathrm{velocity} \\ \mathrm{Dimensional}\mathrm{formula}: \\ \mathrm{p}=\mathrm{mv} \\ =\left[\mathrm{M}\right]\left[{\mathrm{LT}}^{-1}\right] \\ =\left[{\mathrm{MLT}}^{-1}\right] \\ ------------------------- \\ \mathrm{Moment}\mathrm{of}\mathrm{force}:\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{force}\mathrm{and}\mathrm{distance}. \\ \mathrm{Dimensional}\mathrm{formula}=\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]\left[\mathrm{L}\right] \\ =\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right] \\ ------------------------- \\ \mathrm{Work}:\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{force}\mathrm{and}\mathrm{displacement} \\ \mathrm{Dimensional}\mathrm{formula}=\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]\left[\mathrm{L}\right] \\ =\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right] \\ ------------------------- \\ \mathrm{Power}:\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{work}\mathrm{done}\mathrm{per}\mathrm{unit}\mathrm{time} \\ \mathrm{Dimensional}\mathrm{formula}=\frac{\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]}{\left[\mathrm{T}\right]} \\ =\left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-3}\right] \end{gathered}$$