The percentage errors in the measurement of mass ( M ), length ( L...

The maximum percentage error in a quantity with dimensional formula $[M^a L^b T^c]$ is given by $a(\%\text{ error in } M) + b(\%\text{ error in } L) + |c|(\%\text{ error in } T)$.

A. Linear momentum $[M L T^{-1}]$:
$\%\text{ error} = 1(1\%) + 1(2\%) + 1(3\%) = 6\%$ (Matches III)

B. Force $[M L T^{-2}]$:
$\%\text{ error} = 1(1\%) + 1(2\%) + 2(3\%) = 9\%$ (Matches I)

C. Kinetic energy $[M L^2 T^{-2}]$:
$\%\text{ error} = 1(1\%) + 2(2\%) + 2(3\%) = 11\%$ (Matches IV)

D. Power $[M L^2 T^{-3}]$:
$\%\text{ error} = 1(1\%) + 2(2\%) + 3(3\%) = 14\%$ (Matches II)

Therefore, the correct matching is A-III, B-I, C-IV, D-II.

Answer: A-III, B-I, C-IV, D-II