Question

A capillary tube made of glass of radius $0.15mm$ is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05N{m}^{-1}$, density $=667kg{m}^{-3}$) which rises to height $h$ in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of $60°$ with one another. Then $h$ is close to ($g=10m{s}^{-2}$).

• A. $0.172m$
• B. $0.049m$
• C. $0.087m$
• D. $0.137m$

Answer 1

The correct option is C

$0.087m$

Step 1. Given data

Radius of the tube, $r=0.15mm$

Surface tension, $T=0.05N{m}^{-1}$

Density, $\rho =667kg{m}^{-3}$

Step 2. Finding the height, $h$

By using the formula,

$h=\frac{2T\cos \theta }{\rho gr}$ [$g=10m{s}^{-2}$] [$\theta$ is angle of contact and it will be half of the angle$60°$]

$h=\frac{2\times 0.05\times \cos 30°}{667\times 10\times 0.15\times {10}^{-3}}$

$h=0.087m$

Hence, the correct option is $\left(C\right)$.