Physics - Unit & Dimension Question with Solution | TestHub

Impulse $=F\times t$ $$=\frac{m\left(v_2-v_1\right)}{t}\times t=m\left(v_2-v_1\right)$$ $=$ change in momentum $\therefore$ [Impulse $]=[$ Momentum $]$ Angular momentum, $\mathrm{L}=mvr$ Planck's constant, $[h]=[$ energy $]\times [$ time $]$ $$\Rightarrow [F\times r\times \text{ time })=\frac{m\left(v_2-v_1\right)}{t}\times r\times t$$ $\Rightarrow m\left(v_2-v_1\right)\times r=($ change of momentum $)\times r$ $\therefore [h]=[L]$. Work, $W=\vec{F}\cdot \vec{d}:$ Torque, $\tau =\vec{r}\times \vec{F}$ $$\therefore [W]=[\tau ]$$ Moment of inertia, $I=m{r}^2=\mathrm{mass}\times (\text{ distance }{)}^2$ Moment of force, $\tau =\vec{r}\times \vec{F}=$ distance $\times$ force $$\begin{array}{rl}& =\text{ distance }\times \frac{\text{ change of momentum }}{\text{ time }}\\ & \therefore [\mathrm{I}]\ne [\tau ].\end{array}$$ Therefore, moment of inertia and moment of force have different dimensions.