Physics - Unit & Dimension Question with Solution | TestHub

Force $F=at+b{t}^2$ From principle of homogeneity, Dimensions of $at=$ dimensions of $F$ $\therefore$ Dimensions of $a=\frac{[F]}{[t]}=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{[\mathrm{T}]}$ $=\left[{\mathrm{MLT}}^{-3}\right]$ Similarly, dimensions of $b=\frac{[F]}{\left[t^2\right]}=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[{\mathrm{T}}^2\right]}=\left[{\mathrm{MLT}}^{-4}\right]$