Question

Find the difference in heights in limbs as shown in the given data. Surface tension $T=7.3\times {10}^{-2}N/m$, the density of water $\rho =1000Kg/m^3$ and the angle of contact $\theta =0°$.

• A. $1.19m$
• B. $2.19m$
• C. $3.19m$
• D. $4.19m$

Answer 1

The correct option is B

$2.19m$

Step 1. Given data

Surface tension $T=7.3\times {10}^{-2}N/m$

The density of water $\rho =1000Kg/m^3$

The angle of contact $\theta =0°$.

Step 2. Comparing pressure at points $A$and point $B$

We have, $P_0$ is the pressure above the fluid

$\rho$ is the density of the fluid

$g$ is the acceleration of the object due to gravity

$h_1$is the height of the column of fluid at a point $A$

$h_2$ is the height of the column of fluid at a point $B$

$T$ is the Surface tension

$R_1$ is the width of the tube at a point $A$

$R_2$ is the width of the tube at a point $B$

$$\begin{gathered} P_o-\frac{2T}{R_1}+h_1\rho g=P_o-\frac{2T}{R_2}+h_2\rho g \\ \left(h_1-h_2\right)\rho g=2T\left[\frac{1}{{\displaystyle \frac{5}{2}}\times {10}^{-3}}-\frac{1}{{\displaystyle \frac{8}{2}\times {10}^{-3}}}\right] \\ {h}_1-h_2=2\times 7.3\times \frac{{10}^{-2}}{1000\times 10\times {10}^{-3}}\times \frac{3}{20} \\ =2.19mm \end{gathered}$$

Hence, the correct option is (B).