Match List-I with List-II.
Choose the correct answer from the options given below:
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To match physical quantities with their units, use dimensional analysis. Dimensional analysis helps in determining the correct formula and unit for each physical quantity.
(A) Young's Modulus: Young's modulus is defined as the ratio of stress to strain. The SI unit is \( \frac{\text{Force}}{\text{Area}} = \frac{MLT^{-2}}{L^2} = M L T^{-2} \), corresponding to (I).
(B) Torque: Torque is calculated as the product of force and distance. Given the SI unit of force is \( M L T^{-2} \) and the unit of distance is \( L \), the SI unit of torque is \( M L^2 T^{-2} \), corresponding to (II).
(C) Coefficient of Viscosity: The coefficient of viscosity is the ratio of force per unit area to the rate of velocity change. Its unit is \( M L^{-1} T^{-1} \), corresponding to (I).
(D) Gravitational Constant: The gravitational constant's unit is \( M^{-1} L^3 T^{-2} \), corresponding to (IV).Therefore, the correct option is (4).
