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Q.

A container contains two immiscible liquids of density $ρ_{1}$ & $ρ_{2}$ ( $ρ_{2} > ρ_{1}$ ). A capillary of radius r is inserted in the liquid so that its bottom reaches upto denser liquid. Denser liquid rises in capillary & attain height equal to h which is also equal to column length of lighter liquid. Assuming zero contact angle find surface tension of heaver liquid

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a

$2 π r ρ_{2} g h$

b

$2 π r (ρ_{2} - ρ_{1}) g h$

c

$\frac{r}{2} (ρ_{2} - ρ_{1}) g h$

d

$\frac{r ρ_{2} g h}{2}$

answer is C.

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Detailed Solution

Equating pressure at upper level of liquid 2.

$P_{0} - \frac{2 S}{r} + ρ_{2} g h = P_{0} + ρ_{1} g h$

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A container contains two immiscible liquids of density ρ1 & ρ2 (ρ2>ρ1 ). A capillary of radius r is inserted in the liquid so that its bottom reaches upto denser liquid. Denser liquid rises in capillary & attain height equal to h which is also equal to column length of lighter liquid. Assuming zero contact angle find surface tension of heaver liquid