Match List I with List II regarding the excess force required to...

The excess force required to detach an object from a liquid surface is given by $F = T \times L_{\text{eff}}$, where $L_{\text{eff}}$ is the effective length of the boundary in contact with the liquid.

A. Circular disc of radius $r$: The liquid touches only the outer perimeter. $L_{\text{eff}} = 2\pi r$. Excess force = $2\pi rT$. (Matches IV)

B. Circular ring of radius $r$: The liquid touches both the inner and outer perimeters. $L_{\text{eff}} = 2\pi r + 2\pi r = 4\pi r$. Excess force = $4\pi rT$. (Matches III)

C. Square plate of side $a$: The liquid touches only the outer perimeter. $L_{\text{eff}} = 4a$. Excess force = $4aT$. (Matches II)

D. Square frame of side $a$: The liquid touches both the inner and outer perimeters. $L_{\text{eff}} = 4a + 4a = 8a$. Excess force = $8aT$. (Matches I)

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

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