Physics - Unit & Dimension Question with Solution | TestHub

(A) $[\mathrm{Y}]=\frac{\mathrm{F}}{\mathrm{A}\left(\frac{\Delta \ell }{\ell }\right)}\Rightarrow \frac{{\mathrm{MLT}}^{-2}}{{\mathrm{L}}^2}={\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}$ (B) Torque $(\vec{\tau })=\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{F}}$ $(\vec{\tau })=\mathrm{L}\times {\mathrm{MLT}}^{-2}={\mathrm{ML}}^2{\mathrm{T}}^{-2}(\mathrm{IV})$ (C) Coefficient of viscosity $\Rightarrow F=\eta A\frac{dV}{dt}$ $\eta \to \mathrm{Pa}\cdot \sec$ $[\eta ]=\frac{{\mathrm{MLT}}^{-2}}{{\mathrm{L}}^2}\times \mathrm{T}={\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}$ (D) Gravitational constant (G) $\begin{array}{rl}& \mathrm{F}=\frac{{\mathrm{GM}}_1{\mathrm{M}}_2}{{\mathrm{r}}^2}\\ & [\mathrm{G}]=\frac{\mathrm{F}\cdot {\mathrm{r}}^2}{{\mathrm{m}}_1{\mathrm{m}}_2}=\frac{{\mathrm{MLT}}^{-2}\times {\mathrm{L}}^2}{{\mathrm{M}}^2}={\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\end{array}$