Match List - I with List - II. List - I List - II (A) Young's Modulus (I) \(M{L}^{-1}{T}^{-1}\) (B) Torque (II) \(M{L}^{…

\(\text{ (A) }[Y]=\frac{F}{A\left(\frac{\Delta ℓ}{ℓ}\right)}=M{L}^{-1}{T}^{-2}\left(\frac{\Delta ℓ}{ℓ}\right.=\text{ Dimensionless })\)

(B) Torque

\((\vec{\tau })=\vec{r}\times \vec{F}=L\times ML{T}^{-2}=M{L}^{2}{T}^{-2}\)

(C) Coefficient of viscosity \(\Rightarrow \frac{F}{A\cdot \frac{dv}{dt}}\)

\(\eta \to Pa\text{ sec. }\\ [\eta ]=\frac{ML{T}^{-2}}{{L}^{2}}\times T=M{L}^{-1}{T}^{-1}\)

\(\text{ (D) Gravitational constant ( }G\text{ ) }\\ [G]=\frac{F\cdot {r}^{2}}{{m}_{1}{m}_{2}}=\frac{ML{T}^{-2}\times {L}^{2}}{{M}^{2}}={M}^{-1}{L}^{3}{T}^{-2}\)