Match List-I with List-II, where List-II gives the dimensional formulas of the physical quantities in List-I when Energy ( E ), Momentum ( P ), and Force ( F ) are chosen as the fundamental quantities. List-I List-II (A) Mass (I) [E F⁻¹] (B) Time (II) [P^2 E⁻¹] (C) Length (III) [E⁻¹ F^2] (D) Surface Tension (IV) [P F⁻¹] Choose the correct answer from the options given below:

Step-by-step solution

Let us express the standard fundamental quantities (Mass, Length, Time) in terms of Energy ( E ), Momentum ( P ), and Force ( F ). The standard dimensional formulas are: [E] = [ML^2 T⁻²] [P] = [MLT⁻¹] [F] = [MLT⁻²] To find Length ( L ): [E] [F] = [ML^2 T⁻²] [MLT⁻²] = [L] So, [L] = [E F⁻¹] . This matches (C) with (I). To find Time ( T ): [P] [F] = [MLT⁻¹] [MLT⁻²] = [T] So, [T] = [P F⁻¹] . This matches (B) with (IV). To find Mass ( M ): Since kinetic energy E = P^2 2M , we have M P^2 E . Dimensionally, [P]^2 [E] = [M