Physics - Unit & Dimension Question with Solution | TestHub

$$\mathrm{F}=\mathrm{A}\sin \mathrm{Ct}+\mathrm{B}\cos \mathrm{Dx}$$ Since the argument of trigonometric functions is the angle, which is dimensionless $$\begin{array}{rl}& \therefore [\mathrm{Ct}]={\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\\ & \Rightarrow \left[{\mathrm{CT}}^1\right]={\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\\ & \Rightarrow [\mathrm{C}]={\mathrm{T}}^{-1}...(1)\end{array}$$ Similarly $$\begin{array}{rl}& [\mathrm{Dx}]={\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\\ \Rightarrow & \left[{\mathrm{DL}}^1\right]={\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\\ \Rightarrow & [\mathrm{D}]={\mathrm{L}}^{-1}...(2)\end{array}$$