Question

water rises in a capillary tube to a height of 2 cm.In another capillary tube whose radius is one third of it,how much will the water rise ?If the first capillary tube is inclined at an angle 60 with the vertical , then what will be the position of water in the tube?

Answer 1

we know , height of liquid column in a capillary tube is inversely proportional to its radius, r.
so, the relation between heights and radii are given by, $h_1r_1=h_2r_2$

a/c to question,
$h_1=2cm,r_2=\frac{1}{3}r_1$
thus, $2r_1=h_2\frac{1}{3}r_1$
$h_2=6cm$
hence, water rises 6cm.

in the 2nd case,
if the water rises upto a length l in the tube , then vertical height h must be the same as in $l=\frac{h}{cos\theta}$

where $\theta$ is the inclined angle of a capillary tube with vertical.

so, l = 2cm/cos60° = 4cm