Question

Match List-I with List-II.

Choose the correct answer from the options given below:

• A. (A)-(I), (B)-(III), (C)-(I), (D)-(II)
• B. (A)-(II), (B)-(IV), (C)-(II), (D)-(III)
• C. (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
• D. (A)-(I), (B)-(II), (C)-(I), (D)-(IV)

Hint:

To match physical quantities with their units, use dimensional analysis. Dimensional analysis helps in determining the correct formula and unit for each physical quantity.

Answer 1

The Correct Option is D

(A) Young's Modulus: Young's modulus is the ratio of stress to strain. Its SI unit is \( \frac{\text{Force}}{\text{Area}} = \frac{MLT^{-2}}{L^2} = M L T^{-2} \), which corresponds to (I).

(B) Torque: Torque is the product of force and distance. The SI unit of force is \( M L T^{-2} \), and the unit of distance is \( L \), so the SI unit of torque is \( M L^2 T^{-2} \), which corresponds to (II).

(C) Coefficient of Viscosity: The coefficient of viscosity is the ratio of force per unit area to the rate of change of velocity. Its unit is \( M L^{-1} T^{-1} \), which corresponds to (I).

(D) Gravitational Constant: The gravitational constant has the unit \( M^{-1} L^3 T^{-2} \), which corresponds to (IV). Thus, the correct answer is option (4).