Question

If the capillary rise of water in a 1 mm diameter tube is 3 cm, the height of capillary rise of water in a 0.2 mm diameter tube in cm will be -

• A. $1.5$
• B. $7.5$
• C. $15$
• D. $75$

Answer 1

The correct option is C $15$

$\text{Capillary rise in a capillary tube, h}=\frac{4Tcos\theta }{\rho gd}$
Where T= Surface tension
$\theta =\text{Contact angle}$
$\rho =\text{Density of liquid}$
d= Diameter of the capillary tube
Hence, $h\propto \frac{1}{d}$
$\frac{h{}_1}{h{}_2}=\frac{d{}_2}{d{}_1}$
$\text{Data given}:d{}_1=1mm,h_1=3cm,d_2=0.2mm$
$hence{h}_2=\frac{h{}_{1}d{}_1}{d{}_2}=\frac{3\times 1}{0.2}cm=15cm$