Match the LIST-I with LIST-II

Choose the correct answer from the options given befow:

Spring constant:

$$F=kx\Rightarrow k=\frac{F}{x}$$

$$[k]=\frac{MLT^{-2}}{L}=[MT^{-2}]$$

So, (A) matches with (II)

Thermal conductivity:

From Fourier’s law:

$$\frac{Q}{t}=kA\frac{\Delta T}{L}$$

$$k=\frac{Q}{t}\cdot\frac{L}{A\Delta T}$$

$$[Q]=ML^2T^{-2}$$

$$[k]=\frac{ML^2T^{-2}}{T}\cdot\frac{L}{L^2\cdot K}=[MLT^{-3}K^{-1}]$$

So, (B) matches with (IV)

Boltzmann constant:

$$E=k_BT$$

$$\left[K_B\right]=\frac{E}{T}=\frac{ML^2T^{-2}}{K}=[ML^2T^{-2}K^{-1}]$$

So, (C) matches with (I)

Inductive reactance:

$$X_L=\omega LXL​=ωL$$

$$[X_L]=[\text{resistance}]=[ML^2T^{-3}A^{-2}]$$

So, (D) matches with (III)

Final matching:

(A)−(II), (B)−(IV), (C)−(I), (D)−(III)