A capillary type tube AB is connected to a manometer M as shown i… - Vidyadip

MCQ

A capillary type tube $AB$ is connected to a manometer $M$ as shown in the figure. Stopper $S$ controls the flow of air. $AB$ is dipped into a soap solution where surface tension is $T$ . On opening the stopper for a while, a bubble is formed at $B$ end of the manometer and the level difference in manometer limbs is $h$ . If $P$ is the density of manometer soap solution and $r$ the radius of curvature of bubble, then the surface tension $T$ of the liquid is given by ...

A
$2r\ \rho gh$
B
$4r\ \rho gh$
C
$r\ \rho gh$
✓
$\frac{{r\rho gh}}{4}$

✓

Answer

Correct option: D.

$\frac{{r\rho gh}}{4}$

d
Pressure at $\mathrm{B}=$ Pressure $\mathrm{E}$

$\mathrm{P}_{0}+\frac{4 \mathrm{T}}{\mathrm{r}}=\mathrm{P}_{0}+\rho \mathrm{gh}$

$\mathrm{T}=\frac{\mathrm{rpgh}}{4}$

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