Match List - I with List - II.

Choose the correct answer from the options given below :

Young’s modulus:

$$Y=\frac{\text{stress}}{\text{strain}}$$

Strain is dimensionless, so

$$[Y]=[\text{stress}]=\frac{\text{Force}}{\text{Area}}=\frac{MLT^{-2}}{L^2}=[ML^{-1}T^{-2}]$$

So, (A) matches with (II)

Torque:

$$\tau=r\times F$$

$$[\tau]=[L]\cdot[MLT^{-2}]=[ML^2T^{-2}]$$

So, (B) matches with (IV)

Coefficient of viscosity:

$$[\eta]=[ML^{-1}T^{-1}]$$

So, (C) matches with (I)

Gravitational constant:

From Newton’s law:

$$F=\frac{GMm}{r^2}\Rightarrow G=\frac{Fr^2}{Mm}$$

$$[G]=\frac{MLT^{-2}\cdot L^2}{M^2}=[M^{-1}L^3T^{-2}]$$

So, (D) matches with (III)

Final matching:

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