The percentage errors in the measurement of mass ( M ), length ( L ), and time ( T ) are 1 % , 2 % , and 3 % respectively. Match the physical quantities in List-I with the maximum percentage error in their calculated values in List-II. List-I List-II A. Linear momentum I. 9 % B. Force II. 14 % C. Kinetic energy III. 6 % D. Power IV. 11 %

Step-by-step solution

The maximum percentage error in a quantity with dimensional formula [M^a L^b T^c] is given by a( % error in M) + b( % error in L) + |c|( % error in T) . A. Linear momentum [M L T⁻¹] : % error = 1(1 %) + 1(2 %) + 1(3 %) = 6 % (Matches III) B. Force [M L T⁻²] : % error = 1(1 %) + 1(2 %) + 2(3 %) = 9 % (Matches I) C. Kinetic energy [M L^2 T⁻²] : % error = 1(1 %) + 2(2 %) + 2(3 %) = 11 % (Matches IV) D. Power [M L^2 T⁻³] : % error = 1(1 %) + 2(2 %) + 3(3 %) = 14 % (Matches II) Therefore, the correct matching is A-III,