A container is partially filled with a liquid of density . A capillary tube of radius is vertically inserted in this liquid.

Question

A container is partially filled with a liquid of density $ρ_{2}$ . A capillary tube of radius $r$ is vertically inserted in this liquid. Now another liquid of density $ρ_{1} (ρ_{1} < ρ_{2})$ is slowly poured in the container to a height $h$ as shown. There is only denser liquid in the capillary tube. The rise of denser liquid in the capillary tube is also $h$ . Assuming zero contact angle, the surface tension of heavier liquid is

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(3)

$P_{0} + ρ_{1} g h - ρ_{2} g h + \frac{2 T}{r} = P_{0} \Rightarrow T = \frac{r}{2} (ρ_{2} - ρ_{1}) g h$

Solution

1 $r ρ_{2} g h$

2 $2 π r ρ_{2} g h$

3 $\frac{r}{2} (ρ_{2} - ρ_{1}) g h$

4 $2 π r (ρ_{2} - ρ_{1}) g h$

Ans.
(3)

$P_{0} + ρ_{1} g h - ρ_{2} g h + \frac{2 T}{r} = P_{0} \Rightarrow T = \frac{r}{2} (ρ_{2} - ρ_{1}) g h$

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Solution

1 rρ2gh

2 2πrρ2gh

3 r2(ρ2-ρ1)gh

4 2πr(ρ2-ρ1)gh