Match List-I with List-II. List-I List-II (A) Gravitational...

(A) Gravitational constant ($G$): $F = \dfrac{G m_1 m_2}{r^2} \Rightarrow G = \dfrac{F r^2}{m_1 m_2}$
Dimensions of $G = \dfrac{[\mathrm{MLT}^{-2}][\mathrm{L}^2]}{[\mathrm{M}^2]} = [\mathrm{M}^{-1}\mathrm{L}^3\mathrm{T}^{-2}]$

(B) Planck's constant ($h$): $E = h\nu \Rightarrow h = \dfrac{E}{\nu}$
Dimensions of $h = \dfrac{[\mathrm{ML}^2\mathrm{T}^{-2}]}{[\mathrm{T}^{-1}]} = [\mathrm{ML}^2\mathrm{T}^{-1}]$

(C) Coefficient of viscosity ($\eta$): $F = \eta A \dfrac{dv}{dx} \Rightarrow \eta = \dfrac{F}{A \left(\dfrac{dv}{dx}\right)}$
Dimensions of $\eta = \dfrac{[\mathrm{MLT}^{-2}]}{[\mathrm{L}^2][\mathrm{T}^{-1}]} = [\mathrm{ML}^{-1}\mathrm{T}^{-1}]$

(D) Specific heat capacity ($c$): $Q = mc\Delta T \Rightarrow c = \dfrac{Q}{m\Delta T}$
Dimensions of $c = \dfrac{[\mathrm{ML}^2\mathrm{T}^{-2}]}{[\mathrm{M}][\mathrm{K}]} = [\mathrm{M}^0\mathrm{L}^2\mathrm{T}^{-2}\mathrm{K}^{-1}]$

Therefore, the correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Answer: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)