Two parallel plates of width 'W' (see figure) are vertically inserted in a perfectly wetting liquid of density ' ρ '. The separation between the plates is ' d ' ( d ≪ W )

Question

Two parallel plates of width 'W' (see figure) are vertically inserted in a perfectly wetting liquid of density ' $ρ$ '. The separation between the plates is ' d ' $(d ≪ W)$ . The liquid rises in between the plates and becomes static. If surfaces tension of liquid is 'S' then

List - I	List - II
(I) Height risen in between the plates is given by	(P) Zero
(II) The heat energy released in the process of rising liquid	(Q) $\frac{4 S ^{2} ω}{ρ gd}$
(III) The force of attraction between the plates	(R) $\frac{2 S}{ρ gd}$
(IV) The work done by surface tension in raising the liquid	(S) $\frac{2 S ^{2} ω}{ρ gd ^{2}}$
	(T) $\frac{2 S ^{2} ω}{ρ gd}$

TestHub · Accepted Answer

Surface-tension force supports the column: $2 S W = ρ (d hW) g \Rightarrow h = \frac{2 S}{ρ g d}$

Work by surface tension: $W_{ST} = 2 S W \cdot h = \frac{4 S ^{2} W}{ρ g d}$

Gravitational PE stored: $W_{g} = \frac{1}{2} (ρ d hW g) h = \frac{2 S ^{2} W}{ρ g d}$

Heat released $Δ H = W_{ST} - W_{g} = \frac{2 S ^{2} W}{ρ g d}$ ; force of attraction $F = \frac{2 S ^{2} W}{ρ g d ^{2}}$ . This matches option C.

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