Question

Water rises to a height of 10 cm in a capillary tube and mercury falls to a depth of 3.5 cm in the same capillary tube. The density of mercury is 13.6 gm/cc and its angle of contact is 135°, also density of water is 1 gm/cc and its angle of contact is 0°, then the ratio of surface tension of the two liquid is ______.

(cos 135° = 0.7)

Options

• 1: 14

• 5: 34

• 1: 5

• 5: 27

Answer 1

Water rises to a height of 10 cm in a capillary tube and mercury falls to a depth of 3.5 cm in the same capillary tube. The density of mercury is 13.6 gm/cc and its angle of contact is 135°, also density of water is 1 gm/cc and its angle of contact is 0°, then the ratio of surface tension of the two liquid is 5: 34.

Explanation:

h= `(2"T" cos theta)/("rpg")`

T= `("hrpg")/( 2cos theta) ⇒ "T" alpha "hp"/(cos theta)`

∴ `"T"_"W"/"T"_"M"+ "h"_"W"/"h"_"M"xx"p"_"W"/"p"_"M"xx cos theta_"M"/cos theta_"W"`

=`10/3.5xx1/13.6xxcos135/costheta`

= `{10xx0.7)/(3.5xx13.6)`

=`10/86`

=`5/34`